For me it's a show that's outstanding and I can rewatch many times over, but some people are stricter or more relaxed than me, some have the caveat of the show having to be "timeless" or "a classic". I'd love to hear different takes on what a 10/10 actually means.
A 10/10 is something that has affected me on a personal level, and it would be something that I will likely remember for the rest of my life. While many shows are amazing and entertaining, a 10/10 is basically an experience "imprinted" in my brain and is therefore dedicated only for the special ones.
For me I found a anime that was a standard for a 10 out of 10, then adjusting my scores centered around that. I think that being Trigun, that being said it is a classic and at that point I had not watched many anime. More recently I added ID: INVADED as a 10 out of 10, which finished airing this year. Like you said the anime that I give a 10 out of 10 I could rewatch countless times and not get bored of it. Something that is outstanding, that has a different feeling than other anime, a anime that makes you feel happy whenever you watch it. That is when I feel it is appropriate to give an anime a 10 out of 10.
I rate out of enjoyment. A 10/10 for me is a series I watched and didn't have any complaints that weren't nitpicks. A series where I got completely immersed, attached to the characters and couldn't wait to see what happens next. It could be an action series with a plot I loved (Fate/Zero) or a comedy with writing that constantly made me laugh with character interactions (KonoSuba). It could also be a series that gripped me emotionally (Kimi no Na wa).
Outside of these factors, other thing that can influence a 10/10 for me are the music (ambient, OP/ED), animation quality and how well the series set out to do what it aimed to do. Of course, these factors only apply to anime and not manga.
Specifically speaking on manga, I rate pretty much only on what I wrote at the top. How well it can make me feel like I'm in the world rather than looking at panels on a page is the biggest factor I can think of that wasn't mentioned above.
So basically, a 10/10 is a series that I couldn't put down and that I feel was incredibly enjoyable.
I personally use the 5 star system since its more vague if that makes any sense.
something can be 5 stars while not being a total 10/10. I've positioned it as a ranking for shows/movies that i loved or strongly recommend to others.
Example for me would be while Ascendence of a Bookworm , Re:Zero, or Little Witch Academia wouldn't be 10/10, I loved them alot and felt like they deserved the 5 star rating.