Electrical and wiring in fuse box
You have a degraded or broken neutral wire.  This is an emergency and you should shut off main power immediately!    This may be a power company problem which they would need to fix. 

North American power is provisioned by two "hot" legs 240V apart, and a neutral in the middle.  If the neutral fails, then the hot-hot voltage will still be 240V.  However, the neutral will be untied, and will "wander around", not being in the middle anymore.  If loads are exactly equal on both sides, it will be near 120V.  However usually, loads are unequal, often quite unequal, and that will pull neutral off center.  This will undervoltage some appliances which is sometimes dangerous, and overvoltage some appliances, which is often dangerous!

There's a complication.  Inside your main panel, neutral is bonded to a grounding system to a ground rod or water pipe in the earth.  Meanwhile your neighborhood has a supply transformer a couple of poles away from hour house.  This transformer also connects its neutral tap to a ground rod out there at the pole.  Your neutral current is trying to return via this path.  It's a very poor path, so when you load up your system you are overloading it. You are also electrifying your grounding system and the soil around your house!   Obviously this is a very bad thing to do.

If the problem is evident inside your main panel, call the power company and ask them to fix it quick.  It might be a problem inside the main panel where the neutral wire splices to the panel.  But more likely it's out in the meter housing or the wiring drop to your house, which makes it definitely in the power company's bailiwick.  (they might be happy fixing a neutral problem in your main panel too, if you seem like a DIY type; messing with the neutral is dangerous if anything is energized.)