Logical and extended partitions are derivatives of the (legacy) MBR [master boot record] disks. They refer to a virtual partition that exists in the extended physical partition of a drive. The only thing that limits the size of a logical partition and how many you have is the extended partition and its size on the drive.
GPT [general or generic partition table] disks can have an unlimited number of primary partitions, making logical and extended partitioning really only good for virtual machines, if you wanted a dedicated partition for that.
Primary partitions are the only partition capable of having the boot attribute set for the bios to utilize. As aravisian said, primary partitions are the only bootable partitions.
You can place home and any data partitions in extended. Efi, swap and system partitions must be primary.