The Linux swap partition is similar to the Windows swap file, but unlike Windows, Linux does not use it if it is not needed.
A 64-bit Windows system with 4GB RAM will automatically have a 4GB swap file created, and a similarly sized hibernation file. When Windows starts, the swap file is populated whether it is needed or not, but being hard disk based, it is approximately 20-30 times slower than RAM, so any files read to or from the swap file will be done very slowly. When Windows enters hibernation, data that is not contained in the swap file but in use by the OS is copied to the hibernation file, so at any time, that windows system can have up to 8GB of hard disk space consumed by "system resources"
Linux systems use the system RAM more efficiently, sequentially filling it until no space remains, then when more is required, the swap partition is used. If a Linux system starts to use the swap space, it is quite noticeable because the operator will see a definitive slow-down until the memory is freed up, but to give that perspective, in my 7 years of using Linux, I have only ever had 120MB of swap used during some very heavy workloads on a system with 3GB installed RAM
When a Mepis Linux system hibernates, it usually uses the RAM and drops battery consumption considerably. An Asus eee netbook can go for a week in hibernation without totally exhausting the battery, but some users prefer to use the swap partition instead, which makes it possible to hibernate without consuming any battery power at all, hence the advice to have a swap partition in most laptops.