The player character gets this condition when the weight of items in their inventory exceeds the allowable carry weight limit, i.e. your character can only carry 100 lbs but has 101 lbs of items in inventory, thus the character has become over-encumbered. To become un-over-encumbered, the player's inventory weight just has to drop to or below the carry weight limit.
Fallout 3 and Fallout: New Vegas
After becoming over-encumbered, your character will not be able to run with this condition but can only do a slow walk. Sneaking is also difficult (and slower still than walking) as the inventory items create noise when moving. Fast travel also becomes impossible. In Fallout: New Vegas, this issue is expedited by the Long Haul perk.
When playing on Survival difficulty, becoming over-encumbered has several negative effect. In addition to Agility and Endurance being lowered by 2, characters will also periodically take damage as long as they remain over-encumbered.