The blue line in football is a computer-generated visual aid that marks the line from where the snap was made at the start of the play, which is the same as the line of scrimmage. The line moves as the play moves, adjusting to wherever the line of scrimmage is for that down. The center will always snap the ball from where the blue line is located.
The line can only be seen on TV broadcasts. Since the game of football is heavily centered around teams' down cycles, it is important for people who are in the stadium or watching it from home to have information such as how many yards are left for a first down, at what down is the team, and where the play is starting from.
While people watching the game at the stadium have objects such as down markers and scoreboards available everywhere, people at home would be left in the dark about important pieces of information such as this, if not for technologies such as the blue line. In TV broadcasts of football games, the blue line comes together with the yellow first down line.