Half guard as the name implies is you  usiare only using “half your guard” as opposed to full or closed guard where you have both legs wrapped around your opponent.

Half guard can take on my different forms such as knee shield, z guard, deep half, coyete  guard but  essentially is you are using one leg inside their leg and one leg out , either in knee frame or behind the opponent’s hamstring.

Half guard is a great early guard to learn how to defend and attack.  Also it is important to learn how to transition to closed guard.

Here are some great co concept videos discussing half guard important half guard concepts.