Your brain has become a pattern detector and now it can't seem to switch off. Once you notice a number sequence, you start actively looking for it without realizing it - and of course you find it more often, because you're looking at the clock with different eyes. It's nothing supernatural, it's just like when you buy a red car and suddenly you see red cars everywhere.
What others don't mention is this: selective attention is incredibly powerful and also dangerous if you let it carry you away too much. If you start searching for deep meanings in every number you see, you risk entering a vicious cycle where everything becomes a "sign" of something. Once you give emotional importance to these moments, your brain actively seeks them out to confirm what you already believe - it's like a self-fulfilling prophecy.
If you want to do a simple test, for one week stop checking the time intentionally and don't search for any numbers. You'll see that the sequences disappear. Or, if you really do notice 11:11 often, start paying attention to all the other random times that have nothing special about them - I bet there are a lot more of those. Statistical coincidence is less fascinating than believing in synchronicity, I know, but that's what's happening.