Basting is a method where you use a liquid to moisten a meat while you are cooking, often roasting it. This liquid could be anything from pan dripping, to melted fat or any other liquid. Basting keeps the meat or other food moist and can improve the colour or flavour of the food which you are cooking.
I used to use a brush with normal bristles for basting food until I discovered a silicone basting brush (pictured). No hairs to fall out and stick to the food and it works much better than you would imagine. Have a Google and find yourself one.
This type of brush works fine for glazing pastry with beaten egg.