This is an important persuasive device. It is simple, too! In any argument or attempt at persuasion, there will usually be a common endpoint upon which all parties will agree.

When you try to establish common ground, you show that you share common beliefs or objectives. This creates a sense that you are, despite your differences, both aiming for a common goal - despite your different means of wanting to reach it, this suggests that - in important and mutually unarguable ways - you are both on the same side.

If you were trying to persuade your teacher that the reason your homework is late is a sound reason, you might try to establish common ground by saying something like, "But, miss, we both want to boost the school's grades, don't we? So I thought that taking a bit of extra time over my homework might help do this...".