Because Rocket and Groot have spent a long time together.
As shown in the film, Groot doesn't just say "I am Groot" in a completely dead voice; there's a lot of emotion and expression behind it. You're probably already able to pick out particularly strong emotions: for example, if he's feeling happy, or sad. What marks Rocket apart is that he can pick up nuance which we can't hear.
The idea that Groot expresses complex ideas through intonation is one supported by the comics. Here's a scene from early in Rocket and Groot's relationship, where Rocket is still confounded by "I am Groot", and Maximus the Mad has to explain it to him:
Here's what Maximus says:
The mature dendritic form of King Groot's people is robust and heavyweight. Often, the organs of acoustic generation become stiff and inflexible. It may sound as if he is simply repeating his name, but that is simply due to the hardened formation of his larynx. You must listen to the sigh of breeze beneath it. The nuance of meaning.
So presumably if you're willing to spend time with Groot and listen, you too would be able to understand what he's saying. This isn't a bond unique to Groot and Rocket (such as telepathy). We don't get details, but we know (MCU) Rocket and Groot have spent a long time together, and presumably this was long enough for Rocket to learn to understand Groot's "speech".
The Wikipedia entry for Groot gives the same explanation:
Maximus the Mad, Black Bolt's brother, asserted that whenever Groot is saying the trademark "I am Groot!" he has actually been saying any number of things, and his varying inflections of the sentence are the equivalent of words and sentences. People who have interacted with Groot are gradually able to decipher the meaning of the inflections and can carry on full conversations with Groot as time goes on.
Now that Guardians of the Galaxy: Vol. 2 is out, proof of this can be found in one of its mid-credits scenes which reveals that, by the time of Avengers: Infinity War, Peter too has learned to understand Groot's speech. So it's not anything special between Rocket and Groot; given enough time, anyone with good hearing can learn to understand what he's saying.