Position where you are laying on your back or side and are controlling one of your opponents legs with one or both of your legs, and your opponent has one or both of his knees on the ground.
Threatening To Stand
Initially, the half-guard would seem to be a terrible position for self-defense since your head is more open to strikes than it is from closed guard. To lower this risk, the bottom half guard player should always be threatening to stand up. This causes your opponent to focus on holding you down which means they aren't able to easily strike you.
All guards in Brazilian Jiu Jitsu (with videos)