Bleedout is the term used when a player has been mortally wounded by the enemy's actions, and lies on the ground awaiting either medical attention or death. A friendly Medic can come and revive them in the midst of a battle, if they have acquired the right perk (Resuscitation). A red skull that slowly begins to drain blood shows how much time is left before you automatically die and are taken to the Respawn page. A medic is able to revive a player if the skull is still draining, but if you bleed out before they reach you, revival is not possible. Pressing the X button will allow you to kill yourself and wait on the Respawn page - But while bleeding out you can look around your body to see if any medics are nearby. You can still see your HUD, so you can tell how much time is left before your whole team respawns. When choosing to press X to respawn, leave 5 seconds from the wave respawn time to assure a fast redeployment.
If you have an enemy who is slowly bleeding out, you can shoot them a few more times or knife them which will cause them to bleedout which, in the stats screen, is counted and called a Finishing Move.
Bleeding Out still counts as a death but being revived lets you get back in the action.