The push-button clasp is a foldover clasp that opens when small, integrated spring-loaded buttons are pressed. This helps secure the buckle closed and reduce inadvertant opening that otherwise may occur when flexing your wrist.
For demonstration purposes only, following are a few sample diagrams of different styles of push-button clasps. As each brand has its own design, the diagrams below do not necessarily reflect the exact buckle design on the selected watch.