Pain in your eyes is not normal. In fact, most of the time the only sensation you should have with your eyes is the sense of movement and slight ocular/orbital pressure when you look hard in one direction. If you are experiencing any sensation of pain, you should see your eye doctor right away. This is what various types of eye pain may be trying to tell you.
Sore with Bright Lights
This usually means that you have been staring at a video or TV screen for too long. Your eyes need a break and they need to rest. They will not get better if you continue staring at various bright screens all day, and the lack of color and movement does not help either. Your eyes were meant to take in a wider, more colorful and visually stimulating field of vision. Walk away from screens every couple of hours to rest those peepers, or, if you can, take a day off from screens entirely. Your eyes should feel much better after that.
Throbbing Pain in and behind the Eyes
Throbbing pain in and/or behind the eyes is often an indication that you have a sinus problem. The human sinuses are located above, below, and behind and in-between your orbital sockets. When you have a cold or a sinus infection, all of the sinuses swell an apply a ton of pressure to your orbital sockets and eyeballs. This makes them throb with pain and nothing will relieve it, short of a good round of antibiotics to kick out the infection and plenty of rest. (At least with a head cold, you know what is causing the pain and pressure and cold medicines will help, whereas a sinus infection is often trickier to detect and more complicated to treat.)
Painful Pressure in the Eyes
When the pain in your eyes is definitely in your eyes, see an eye doctor right away. This could be a sign that you have glaucoma, an eye disease that builds up extra fluid in the eyeballs causing extreme pressure and pain. Your eyes may feel like they are about to explode, but the real problem is with your optic nerves. If pressure is allowed to continue to increase, it can damage your optic nerves and make you blind. Out of all the "pain in your eye" conditions, this one is the most extreme and the worst.