The ME drive is a replacement to the ME chest in that it has the ability to store more than one ME storage item in it. It does not have the chest's interface, however at the point you start using these you should at least have a ME access terminal, so the interface given by the chests become irrelevant. The drives, like their chest counterparts, connect to an ME network either with ME cable or by placing the block next to another block connected to the network.
Each drive may hold up to 10 storage items in it at once, and you may have as many drives as you wish on a single network; much the same as their chest counterparts. The drives, by default, will show how many storage items it contains and the status of each item on the front of the block. And it will show how much types and bytes are used on the back of the block.