Si is a subjective set of internal sensory impressions. Some examples of Si working in the real world, "This food doesn't taste right." You can cook (hypothetically) because you remember seemingly instinctively how to make your favorite meals without a recipe, and know exactly what is "missing" by tasting what you're making. You can tell if something is "off" and doesn't taste the way you know it "should" taste.
Or the picture is crooked. Or this film doesn't align with your particular standards of aesthetics. You may have a very particular preference for how music should sound or how art should look, or a particular flavor of wine you always drink.
You may also store past experiences and facts kind of like a filing cabinet in your mind, and retrieve them in a linear fashion.
Mostly though, Si is an internal set of subjective sensory impressions. It is not the same thing as strength of memory though it does rely on past experience.
Si doms may take great pleasure in knowing every single little detail about their favorite subject or chosen field. They will hesitate and examine new information carefully to see how it aligns with their internal filing cabinet data base.
Si can concern itself often with things like health, safety, and security.
Si related neuroses may manifest in the form of either A) fearing things will always be repetitively the same OR B) conversely, things will be an out-of-control threat to your safety/security/familiar way of being.