What describes how sliding friction affects pushing a cereal box across a tabletop?

Friction is defined as the force that opposes any applied force. Sliding friction affects pushing a cereal box in the sense that you have keep a constant applied force greater than the frictional force on the box to keep it moving. If you stop pushing, the box will stop due to the frictional friction. This is why a box won't keep moving across the table forever after you push it only a brief moment.