4th and 10 is used to describe a scenario in which the offense is on its 4th and final down and needs a full ten yards to gain a first down and keep possession of the ball. When faced with a 4th and 10, the offense will usually elect to punt the ball away to another team, as picking up 10 yards on one play is very challenging and failure to do so may result in the other team taking possession of the ball in scoring range.
To avoid giving the opposing team strong field position by failing to convert a 4th and 10, most teams will elect to punt the ball to the opposing team. In rare cases where the team on offense is losing with little time left to play in the game, the offense will likely stay on the field and try to achieve a first down, often via a long pass.
4th and 10' in football refers to the down and yardage needed for a first down. In this case, it is fourth down and 10 yards are needed to gain another first down. The offense only has four attempts to gain a first down before the ball is given to the opposing team. To gain a first down, the offense must gain 10 total yards of offense. After 10 yards of offense has been achieved, the down is reset to first down and the offense gets four more attempts to gain a first down. The yards needed for a first down are cumulative, so if the offense gained six yards on first down, the next down would be '2nd and 4', meaning it is the second down and they need four yards to get a first down.