There are many forms of DRM - in the old days, you needed the CD/DVD in the drive to start the game up, even if you installed it. That's how dev's + pub's tried to make sure you owned said game.
A few years back - some DRM like newer versions of
Securom only allowed you install a game, activate it online, then the game kept track of X amount of times before you could no longer install it, and now you could actually boot-up your game. And after you ran out of allowed installs, you maybe could revoke a key from a PC (while you're online) to get a +1 back on your allowed install/boot count (if the dev's + publishers allowed for it).
These days, a lot of services are actually DRM. For example, Origin and Steam themselves can be seen as DRM b/c they actually check your account and see if you own a game. And for a lot of games on those services to run, it either phones home to their servers and/or forces you to run their service-program to run their game.
Steam's
CEG is a DRM (which is often optional for dev's + publishers to use) - and it's account-based, where it checks (and often phones home to its server) just to see if you own a game with your account and if you own it, then you can boot-up. Usually, once activated - you can be offline or online and you're good to go to run your game whenever on that particular PC.
Not all games on Steam use CEG - as some games are initially DRM-FREE even on Steam, once you download it - you could run the game from say the game-folder itself or create a shortcut just from there and the game would boot w/out Steam even running (i.e. go see Enslaved, Wizardry 8, and a lot of old-games that use DOSBOX). Some games on Steam might actually not use CEG and instead use other DRM; or might throw additional DRM on-top of Steam, unfortunately.
A lot of games like MMO's (like WoW + The Secret World) & online-only games (like Diablo 3) use some kind of account-based DRM - but, they're in the extreme that you must be online + signed into your account at all times to actually play period.
Also, there is new variation of DRM called
anti-tamper which
Denuvo uses, which often is hard-to-crack b/c it's believed to constantly be encrypting and decrypting files.