What exactly does it mean to have a low blood platelet count?

You can bleed: A low platelet count is called thrombocytopenia. Platelets stick together as part of a clot forming cascade. If you run out of platelets, or any other component, then you will have a hard time stopping any bleeding.

Destruction: It either means that you are not producing them or that your body is decrying them faster than it can produce them. Depending on the level, you may have ncrease risk of bleeding. See a hematologist soon to determine cause which can be many.