When speaking of disk space, a cluster is the smallest possible amount of disk space the file system can allocate.
A file always takes one or more clusters of disk space. For example, if you store a file of 600 bytes to filesystem that allocates disk space in 1024-byte clusters, the file will physically take 1024 bytes. The remaining 424 bytes cannot be used. A file of 1092 bytes will take 2048 bytes physically, and so on.
The reason behind this? Efficiency, of course.
The clusters are mostly an issue in FAT. MS-DOS used rather silly (but efficient at the day) way of organizing the filesystem to clusters whose size depended on disk size. Floppies used 512-byte clusters and hard disks used clusters of multiplies of 1024 - biggest drives needed clusters of 32 kilobytes (or even more, I can't remember)! The amount of disk space wasted by FAT16 was rather tremendous.
FAT32, introduced in Windows 95 OSR2, helped the situation somewhat by decreasing the cluster size on hard drives to 4096 bytes.
Other OSes and filesystems don't need to much worry about clusters and lost space...
See also slack.