Si attaches a sentimentality to a particular memory which makes it more 'memorable' and easy/frequent to recall when something else 'reminds' them.
I have heard it described as a filing cabinet in your brain. Everything is organized by what you have experienced before and you can connect past sensory experiences to new experiences in a direct way. In areas that they are passionate about I have heard it described that they can have an encyclopedia-like knowledge because they like to acquire as much factual information about it as they can to add to their file.
I think with anything there are Si users who have good memories and those who don't. Even if you can't remember specific details I imagine that new experiences would trigger some relationship to past experiences.
^
People tend to water Si down to "oh, it's just nostalgia" and "oh, they have good memories" and basically things that literally everyone can do whether they value Si or not.
I like these two posts. They explain it well.
It's not just "nostalgia." That sounds more like tert Si. It's the sentimentality that goes along with pretty much
everything, completely subconsciously. It's the very lens I look at life through. Everything is connected. A good visual for Si is the roots of a large tree. Above ground, you just see the trunk. Underneath, there is a hell of a lot going on, it's very complex, and it's all connected.
My memory is crap, I can't remember what I did two days ago. Si isn't just "having a good memory." It's more like what ZNP and Verona described.
Si is quite similar to Ni. People recognize how Fi and Ti are similar, but either don't want or refuse to see it with Si and Ni. I use Si with so much ease that it's so difficult to describe. It's like trying to tell someone how to breathe air. I don't have to think about it, I just do it, whether I'm trying to or not.
I relate everything back to something that I've experienced before. Imagine you're trying to teach me to do something completely new to me. I'm going to struggle with it at first. Eventually, something might "click" with me and I'll say, "Oh, so this is kind of like doing [unrelated activity]!" And I'll use all of my experience with
that and be able to apply it to the current activity in a new way.
Sometimes, there's nothing to relate it back to. In which case, I struggle a lot, but eventually through gathering this new experience, I'm able to build up new information and skill that can be applied to future activities that require something similar.
Sure, it seems like something basic anyone can do. So does "having personal values" etc. We all do this. Some of us just do it more.