Hypervigilance means your nervous system is very alert. As kaliope says, one way this is manifested is being on guard for something scary to happen. For example, if I hear a noise, I might immediately attach a scary cause to it: I hear a noise outside the window and feel certain that it is a burglar about to invade my home, when in reality, it's the window blowing through a bush. If you have trouble falling asleep because you are listening to every little sound, or if you have trouble concentrating because small noises or movements distract you, then you may be showing hypervigilance.
Another way hypervigilance manifests itself is through an exaggerated startle response, or jumpiness. If someone drops a book behind you, what do you do? People with typical nervous systems may turn to find the source of the sound; someone with PTSD might jump into the air, shout, or put their hands up. A normal response to terrifying stimuli, but not exactly typical for a dropped book.
You can also be hypervigilant within a relationship, always on guard for people close to you to hurt you. This is particularly common if your trauma was caused by another person. For example, a friend might cancel plans, and instead of thinking, "Oh, she's busy because something came up," I assume, "She hates me and can't stand to spend time with me but I disgust her so much she can't tell me; I should never be friends with anyone!"
Do you see yourself in any of these examples?