Logical Volume management is a means to abstract block devices away from physical devices. In a traditional machine, filesystems are built directly onto the hardware that they are comprised of, so, for instance, the physical number of sectors on a disk will limit how large a filesystem may get, before you will have to create a second filesystem on a separate disk. By adding a separate layer between the blocks presented to the kernel and the physical devices, it allows this limit to be lifted without significant penalty, allowing for filesystems to be able to be constructed as they are desired, and not linked to the physical constraints.
This is only one of the many advantages to LVM. Others include live snapshots, live hardware migration and the ability to expand (and, in some cases, contract) filesystems at will without needing to restart a machine. Some of these actions are explained in detail in the following pages: