activate is a simple program which sets the partition which will be used to boot the system. To be precise, it sets a flag in the partition table of the hard disk. This may or may not have an effect on the bootup procedure. PC booting is complicated, and this manual page does not attempt to explain it; for more information on what partition you should set active, you should consult the documentation for your bootloader (an example bootloader is lilo, which has a good manual in /usr/share/doc/lilo/ on Debian systems).
Note that programs such as fdisk will also allow you to set the active partition; it is probably better to use one of these, since they generally provide services such as allowing you to view the partition table before picking which partition to activate, and provide opportunity to confirm actions before writing to the partition table. However, these programs have more checking for 'wrong' values; for instance, they might not allow you to set the active flag on an extended partition (because this is generally a bad idea). activate, on the other hand, assumes you really do know what you're doing and doesn't have any bothersome prompts or sanity checks. In particular, activate makes no checks that the device you give has a partition table on it at all! If you specify the wrong device it will happily write garbage to it.
partition should be a number between 1 and 4 specifying which partition should have the active flag set.
If no partition number is given, activate will print out the partition which is currently marked active.
lilo comes with extensive documentation; this can be found in /usr/share/doc/lilo/ on Debian systems.