At a basic level, a mountain bike rear suspension will have either one or more pivot points. These pivot points will affect the way the rider pedals and how the suspension will push back.
A common single pivot frame is the Santa Cruz Heckler. It features one pivot a little higher than the bottom bracket.
Double pivot frames feature at least two pivots, though, they have many variants: DW-Link, VPP, Maestro, etc.
Here’s an example of a double pivot frame.