Wot epona said.
The trinity, as it's known, is common language within almost all mmorpg and rpg games. Tank, DPS, Healer. Not all games rely on having a strict trinity, some are a lot more flexible, but it's good to understand the idea behind it so you can adapt it and know what's expected. Even Dragon Age is fashioned around the trinity, although there you're far freer to ignore it altogether if you want.
As epona said, the tank is generally the damage sponge, there to take aggro and get the attention of enemies so that DPS is free to deal all the damage and Healers are free to keep everyone alive (and in some cases provide useful buffs and debuffs). They are your typical knights in shining armour when you think about how they look - heavy armour, brutes, big. That's not always the case when it comes to individual games, but think about it in that way and it's easier to understand what their role is.
DPS (known as DD in ESO, damage dealers) dish out the pain. If min-maxing, they are often glass cannons, meaning they have very little or even nothing in the way of armour and damage mitigation built into their build, and focus solely on pumping up their stats to maximise the damage they can deal with pinpoint accuracy. The tank must work very hard to make sure they keep aggro, because the way the enemy AI usually works is that they'll go after whoever does the most damage. Well you don't want your tanks to be doing the most damage (although they can help), you want your DPS to be doing it, but if the enemy goes after your DPS they'll be dead in a heartbeat. So tanks will have some kind of taunt, which does exactly what it says on the tin - it's a skill or a passive or whatever (depending on the build and the game) that taunts the enemy and makes them so angry at the tank that they only attack them, leaving the DPS free to attack without fear of insta-death. 'Keeping aggro' is a key skill for tanks, and if your build doesn't have the skills to do that, you'll be a crap tank.
Healers keep everyone alive. They generally don't wear much armour, usually because light clothing is often coded to have healing/magic benefits. The idea is a healer won't be doing much damage, if any at all, so they'll likely never draw any aggro (unless the enemy AI is coded to go attack on debuffs, etc). That said, a healer still needs to understand where to stand, to keep out of cc (crowd control) and aoe (area of effect) attacks, otherwise they'll take damage themselves. Healers keep the tank alive, as well as healing any damage the dps may take. Depending on the game, dps might take more damage because it's just not possible for the tank to take it all, but I'm just talking about the pure idea behind the trinity at the moment, not necessarily how it filters down in different games - every game utilises it in its own way. Another role for the healer might be buffing the party - using spells that increase attack speed or stamina regen, or provide better damage mitigation, or poison immunity, etc, for a limited amount of time. Knowing when to fire off those buffs can be crucial. As well as buffs, there are debuffs, that are focused at the enemy to remove whatever positive buffs they have. So a boss might be immune to fire, and a healer might be able to use a debuff which makes a character 50% more susceptible to fire for 20 seconds, for example, or more specifically "removes "Satan's Kiss" for 20 seconds" (idk, making up a name for what an enemy buff that makes them immune to fire damage might be called in a game
). There are also dispels, which are sometimes also called debuffs, which remove negative effects from your party. So, the boss might have cast a snare spell on your party so no one can move, and the healer might have a spell that removes that snare.
Now, each of these roles is flexible depending on the game, and certainly in ESO you only really need to worry about them if you're going to be doing group dungeons and other high level PvE content. It can be useful in Cyrodiil, but your priority is going to be on creating a build that YOU can survive and kill other players with, not on supporting others, unless you join a regular PvP group where you only ever go around together and each has a designated role. For general questing and levelling, you'll want to mostly be dps, but you'll need damage mitigation of some kind (whether it's through passives, armour, spells or all of them) with the understanding that the more tanky you are the longer it'll take to kill things. It's very, VERY useful to have a self-heal of some kind while levelling/questing. That doesn't make you a healer, but you'll be very glad of it. 2H has a skill/passive that heals (epona will be able to tell you what it's called) but if you're a templar then taking the first and/or second healing skill will be all you need while levelling. If you're a stamina build, then you'll never be using magicka, so you'll always have a small reserve of it for an oh shit heal now and again. (You might be using magicka at first for other templar skills but once you morph them I think there are some that can be morphed to use stamina instead.)
Ignore min-maxing unless you really want to be playing at the top levels. And on your first character you absolutely won't be. Min-maxing means people theorycraft their builds so that they can't even eke out 1 single more point of damage/healing/whatever from them, and so each skill and passive and weapon and piece of armour and potion is used for maximum efficiency in synergy with one another. Min-maxing is in no way needed to play the game, even to play it well. It's not needed to do group content, it's not needed to do PvP, and it's certainly not needed to get through the story content. If you do want to go down that route, don't worry about it with your first character. You won't fully understand the game until you've played it through to max level with a character and put in hours and hours to figure out how it plays. Arguably you won't understand the game fully until you've reached max level with every class and every role. But you don't need to if you're not interested in leaderboards and so on.
Back to the trinity: if you do want to pick a role because you expect to do group content, I'd go with dps/dd for now. It's the easiest, which is why there's always a shortage of tanks and healers. There's less to worry about, you just focus on hitting things hard. You worry about you and the enemy, that's all. If you're a tank you have to be aware of aggro all the time, and it can be difficult to keep it on you unless you know what you're doing; it also restricts the types of skills you can take because you HAVE to take taunts and things that help with damage mitigation, whereas with dps you just have to take stuff that deals damage - it's up to you which ones you take to achieve that (there are exceptions - for example some dungeons might need you to have more cc and aoe skills, some might work better if you're only doing single target damage - but in general it's useful to have a mixture of both for hard single enemies and groups of enemies). Healers have to pay attention to everyone in the party all the time, watching for incoming damage, keeping out of damage themselves, watching for buffs, debuffs, negative effects, and of course maintaining the right kind of healing constantly. Of course, playing a tank or healer can be very rewarding, but dps is much easier, and feels very satisfying too. And since you'll be spending most of your time questing, and since it seems you enjoy Cyrodiil a lot, you'll definitely want to be dps with a hint of damage mitigation/survivability, and have a decent self-heal.
and I'm not sure how its triggered.. I guess when the box is completely yellow, but sometimes when I press L1 and R1 nothing happens.
) and flowers, although I can't resist picking them 
