A Primary partition, as the name implies, is the first and most important. A drive can be just one big primary, and nothing else. Primary partitions have a small boot section formatted onto them, which the OS will use for finding the rest of itself, to be able to load up. They also contain the Partition Table, which describes how the drive is divided up.
Extended partition is the other part of the drive, but some systems allow more than one extended one. These generally cannot be used for booting the computer.
Logical drives can be in either type of partition. They are like a real drive in logic (the way they function), but not physically.They cannot be booted from. They are a kind of "super-folder" with their own filing system for tracking folders and files on them. Splitting a large drive into many logicals, for different types of data, can speed up access to the data, as there are smaller indexes to look up each time.