Besides the meanings chris mentioned above, it is worth noting the obvious meaning "I caught/found you" that kinds use when calling out "I got you!" while playing hide-and-seek. Also, when used along an infinitive like "I got you to buy me those fancy shoes", it means "I persuaded you to buy me.../I fooled you into buying me..." Oh, and it can also stand for "I got you covered", as in "I will keep you safe", "I will take care of your needs", or "Everything is under control". Well, the moral of all this is that "I got you" is an extremely common and likely overused expression that can fit in a lot of contexts where it may mean a lot of slightly different things. Rather than trying to memorize all these possible meanings, it is probably wiser to stick to the basic meaning (past tense of "get" = "obtain", "acquire"...) and adjust the meaning to make sense of the specific context you see it in. In time, after some exposure to real-life usage, you'll become confident enough to use it on your own.

it can mean "I understand" or if someone asks you to do something for example, if someone asks you "Can you buy some milk while you are at the grocery store?" you can reply "I got you" meaning that you will do it for them