A balanced line is when there is a guard and a tackle on each side of the center.
An unbalanced line is when either the guard or tackle from one side of the lineup shifts over to the other side of the center.
Offenses do this to make the defense think. The team breaks the huddle and something is different. The Mike/Middle linebacker would likely make a call for the defense to adjust or shift the front. This is all part of the chess game that the Offensice Coordinator & Defensive Coordinator, or the QB & MLB have on every play.
In the balanced line example below, the offense is even with 4 guys on each side of the center counting the receivers. From a defensive perspective there is no “strength” to the formation, so they might call the wide-side of the field the strong side. If the ball is in the middle of the field, they likely go with the set they are most comfortable with.
In the unbalanced line example the offense has 3 men to the left of the center and 5 to the right. The strength is to the right so the defense would call call their left hand side the strong side. It is just a little wrinkle the offense puts in to a) attempt to gain an advantage and b) to make the defense prepare for something else.
Some coaches/schemes/plays call for the guard to shift to the other side, some call for the tackle. In some cases, it’s an extra tight end that is brought into the game that makes a line unbalanced.