If you're new to American Football, you score points in multiple ways, but most well known / commonly is through touchdowns. Touchdowns are made by getting the football, while held in a player's arms, into the endzone area at the end of the field. There are two endzones - you want the ball in the endzone of the way that your team is heading. Getting it in the other one will result in a safety which will give the other team two points as well as posession of the ball.
Upon getting in the endzone, you will secure 6 points and the opportunity at a 7th or 7th/8th if you choose the riskier path of a 2 point conversion. Neither is required in order to unlock the achievement. It will pop at the conclusion of the game.