Hard drive evidence is accessible in two ways - general cached stuff that your browser stores when you browse in normal mode - all the images, videos, streams etc - that's all just there (and very easy to link to IP addresses/etc.), unless you delete it or browse in private mode. If you're browsing in private mode, you should also use a VPN, Tor, or both. (Using a VPN and then connecting to TOR hides the fact that you're connecting to Tor bridges in the first place. Likely be super slow, though.)
Secondly, what happens when you delete stuff normally is that the computer deletes the reference to the stuff. How and where depends on the system, but largely, that's the fastest way to delete stuff from a filesystem - forget it exists. It doesn't automatically actually delete it until the computer happens to overwrite it with new data. You can use secure delete (which overwrites the data on purpose, a varying number of times depending on how secure/slow you want to be) and also 'free space deletion', which overwrites the bits of your drive that aren't actively being used, in the same way, with junk data.
Now, if you have a magnetic drive, rather than a new fangled Solid State Drive, then storing data on the drive leaves a magnetic imprint, even if it's been overwritten by the normal course of use - sort of like seeing the marks from a page above further down in a notepad. The more you overwrite,
the less likely that is.
Eta: Also, most people are horrified to see what their browser gives away about them,
to every single page that asks.
