A sector is a physical spot on a formatted disk that holds information. When a disk is formatted, tracks are defined (concentric rings from inside to the outside of the disk platter). Each track is divided into a slice, which is a sector. On hard drives and floppies, each sector can hold 512 bytes of data.
A block, on the other hand, is a group of sectors that the operating system can address (point to). A block might be one sector, or it might be several sectors (2,4,8, or even 16). The bigger the drive, the more sectors that a block will hold.


So why are there blocks. Why doesn't the operating system just point straight to the sectors? Because there are limits to the number of blocks, or drive addresses, that an operating system can address. By defining a block as several sectors, an OS can work with bigger hard drives without increasing the number of block addresses. For example, PC DOS (earlier versions at least) could only address 65,536 blocks (64K), and each block could only be a single sector. Thus, the largest size a disk volume could be was 32mb (64K * 512bytes). (Earlier versions of the Mac OS had a 16mb volume limit for similar reasons). If you increase the size of a block to, say, 4K, that same version of DOS can now work with volumes as large as 256MB (64K addresses * 4K blocks).
With current versions of the OS's, the formatting software will look at the size of the drive, and figure out the smallest number of sectors that need to be in a block in order to be able to use the entire drive. So, when you format a floppy disk, the block size will be one sector. When you format a 230MB drive, for example, the block size is 8 sectors (4K).  Why does this matter?

True or False: When a file is copied from a hard drive to a floppy, it will usually take up less space than it takes up on a hard drive.

TRUE. Although the size of the file will be the same, fewer sectors will be used to store the file. Conversely, when a file is copied from a floppy to a hard drive, it will usually take up more disk space. When files are stored on a disk, they always use up a whole number of blocks. Any unneeded space at the end of a block is unused and wasted. For example, say your hard drive has a block size of 4K, and you have a file that is 4.5K. This requires 8K to store on your hard drive (2 whole blocks), but only 4.5K on a floppy (9 floppy-size blocks). 
Miscellaneous info...If you tend to store lots of small files on your hard drive (like running Windows and Windows apps), the blocks used to store all those little files can have a lot of wasted space in them. Likewise, compressing lots of little files may not save as much space on a big hard drive with a big block size. If the block size is 4K, and you compress a 3K file, the file will be compressed, but it will still use 4K of disk space. If you do a Get Info on a file on a Mac, the Size info will say something like '12K on disk, 8320 bytes used'. The 12K is the amount of disk space used, based on the block size. Thus, if the block size of your drive is 4K, this number will always be in increments of 4K. 8320 bytes is the actual size of the file. Note that you have to go to Get Info to see the actual size of the file. This number does not show up in View by Name