Back-rank checkmate

This is what a back-rank checkmate is and how to deliver it:

Imagine your king in chess is like a person trapped in a hallway. 
The "back rank": In chess, the back rank is the row closest to you (the 1st rank for White, and the 8th rank for Black).
The "trapped king": Your king is stuck on that back rank.
The "blockers": The reason the king can't escape forward is because its own pieces (often pawns) are in the way on the rank in front of it.
The "attacker": The back rank checkmate happens when a Rook or Queen delivers the check along that back rank. 
So, the back rank checkmate is when your king is trapped on its back rank by your own pieces, and an opponent's Rook or Queen gives it check along that rank, with no escape squares. 
Think of it like this:
Your king is like a car parked in a garage (the back rank) with the garage door (the pawns) blocking its escape. The opponent's Rook or Queen is like a car driving straight down the alleyway (the back rank) and hitting your car (the king) with no way for it to move. 
Why is it important?
It's a common mating pattern: Back rank mates happen frequently, especially at beginner levels.
It highlights a weakness: It shows how leaving your back rank unprotected can be dangerous.
It teaches you to look for escape squares: You learn to create a "flight square" (a square for the king to move to) by advancing one of your back-rank pawns, according to Wikipedia. 
In short, a back rank checkmate is a deadly tactic where your king is trapped by its own pieces on the back rank and then checkmated by a powerful piece.