DRM is basically any form of rights protection, It doesn't always need to slow down your system. You may be thinking of root kits, which install a program that monitors computer activity. (Sony Music had a big scandal about this a few years back)
Blizzard's battlenet is a form of DRM as you need to be online to play Diablo 3, this means you can't give a copy to a mate like you could with diablo 2.
Ubisoft had a few games released last year that need to be online to play them. (Anno 1404)
Steam uses DRM by needing to have a unique account and encrypted game files.
A lot of PC game devs also include 3rd party programs to manage DRM like SecuROM and SafeDisk (not sure how they work tbh, but there is ways around them)
Steam: MrSecro | PSN: Secro