If you look at each individual character, the definitions don't add up. Can someone explain it to me? Also, is this word used often?
真 - really
有 - have
你的 - your/ yours
"真有你的" = "(you) really have your (object implied)"
The object can be 本事，本領，手段 or even 膽色 (ability, skill, means or even balls)
"真有你的" is a common phrase (exclamation) for expressing you are impressed by some's ability, skill, etc.
For example. It is almost impossible to find the first issue of Superman, yet someone managed to find it for you, in this instance, you can say "真有你的，這麽罕見的絕版漫畫你也找得到" (To be able to find such a rare out-of-print comic, You really have yours (ability))"
Example 2: "真有你的，老闆的老闆你也敢約" (Dare to ask your boss's boss out on a date, you really have yours (balls))
Similar to 你真行 (You are great) which also doesn't say great in what aspect
you've really got something (up your sleeves).