Chocobo's are the cute yellow birds which you find in every Final Fantasy. In Final Fantasy VI there is four different types of Chocobo. Two of them can transport you faster than usual without encountering battles while the other two don't.
Yellow chocobos are the normal ones. They can transport your party across land and rivers at twice the normal speed. To mount one press X. Press it again to dismount. Once you get off one, it will run back to the forest.
Black Chocobos can fly low but cannot climb mountains. When in the air they can only land in forests. When you dismount they will wait for you but will go back to their home forest when mounted again.
White Chocobos can fully restore all your MP. At least one lives in every forest(Chocobo forest).
The fattest one of all. The fat chocobo can store items for you. Use a gysahl when the smell of chocobos is in the air and he will appear