What does this mean when someone tells you this?
Are you fucking kidding? Zero context or examples?
Kinda depends on context eg
Student 1: I got you (I’m your assigned study buddy)
Student2 : I got you! (I understand)
Teacher : I got you (I’ve observed that you’re both smoking. Detention for both of you)
You are too kind.(hugs) I told my friend I had sent a letter and wanted to explain and he said i got you. Also, we were walking home and it started raining and I said we I can take it from here, and he said it again.
Depends on context.
“I got what you were saying” is common. When said meanly, it can imply “Shut Up.”
“I figuratively got a hold of you, so I can protect you” is another.
“I got you to believe something that is untrue” (i.e. I tricked you.)
“I got a win against you.”
I’m assuming that this a complete sentence, or you get more varieties.
I got you something: “I procured for you this item”
I got you back: “You did something to me, so I returned the favor.”
There are probably a lot more.
ETA: He’s saying you have been heard or understood. My first guess.
The OP is more suited to MPSIMS rather than General Questions–moved.
samclem Moderator, GQ
Here on the SDMB, it’s spelt “gotcha ya”! 
Without knowing exactly what went on, I’d guess it was definition #1 followed by definition #2
It means I’ll take care of you.
“I understand.”
Still too vague.
Is this in the ‘I’ll provide for all your needs for the rest of your life’ kind of way or the ‘They’ll never find a trace of your remains’ kind of way? 
I Got You Babe
and the complementary:
You Really Got Me
with the somewhat related:
Gotta Get Away (from Me)
Yeah, I was posting from my phone, so I couldn’t really elaborate.
All of the responses here were right…of course there are tons of ways one can mean, “I got you”.
But, being a lover a slang, I went with a popular slang phrase.
If you say, “I want to buy this purse, but I am about 10 bucks short”
I might say, “I got you.” That means I will give you the 10 bucks. Might even mean I will buy the whole purse!
If you say, “I am so stressed and depressed, my man left me, my dog ran away, and I feel so alone and miserable”
I might say, “I got you”. Means, don’t worry, I am here with you, I’ll be a shoulder to lean on, an ear to listen.
If you say, “I’m running late for work! I know I have to have those papers on the boss’ desk by nine!”
I might say, “I got you.” Don’t worry, I’ll get those papers on the desk.
So it just means, I’ll take care of you.
Ah, so sort of like, ‘I got your back’?
I’ve never heard it used like that before, so I guess it depends on your demographic.
Whenever I hear that phrase I think of the really obnoxious ugly woman that Jamie Foxx played in a recurring skit on In Living Color and is why I will forever believe that he should have forfeited any potential Oscars because of that.
Don’t worry about it, Wile E. I got you. Catch phrase at the 4:48 mark. Not that you asked for a link, but just in case. I got you.
It means the exact same thing as its simplification: Gotcha.
In my click it means “I got your back”. As a neighbor and friend. We keep different hours but will always be aware of the block at all times and keep open communication. It also means that you will never be denied a favor. Just the way it should be.
thanks guys. 