Bounding Overwatch, or Leapfrogging is a common tactic used by modern armies for advancing (or retreating) ground troops and vehicles. One part of the unit advances while being covered by another part of the unit.
In X-Com, this translates to part of a fire team saving Time Units while the other part attempts to move forward and/or find cover. The scout or forward element moves forward slowly, using about half its time units to establish firing positions. The rear element may not move at all if the scouts don't see any enemies to engage or cover to move to, or they may move up either to find cover or new firing positions located by the scouts.
If enemies are spotted, the rear element can fire with less risk (on the player turn) than the scouts. The scouts then have time to move to the next cover and repeat the process. The rear element may, in some cases, move forward and become the scout element on the next turn; hence the nickname "leapfrog." On open terrain, the rear element can move nearly as far forward as the scout's position, and the scout may move back slightly to keep any unseen enemies at maximum range. This keeps the team ready for Reactions (on the enemy turn) in the absence of cover.