Encumbrance represents the total amount of weight you are currently carrying. This includes all items in your inventory, whether equipped or not. Carrying more than your maximum Encumbrance will cause you to be unable to move (though you can still fight, cast spells, use items, etc.). Your maximum Encumbrance is equal to your Strength × 5. This means that once you have maxed out your Strength attribute, your maximum Encumbrance will be 100 × 5 = 500.
You can additionally use Fortify Strength effects to increase your carrying capacity yet further. In addition, using Feather effects will lower your current Encumbrance. However, a single point in Feather and a single point in Fortify Strength cost the same amount in terms of Magicka or enchanting points, and since each point in Strength is equivalent to 5 points in Feather, Fortify Strength is clearly the more favorable of the two. (Increased Strength also results in higher damage with melee weapons, another perk.)
Encumbrance also has an effect on your Speed. In this case, it is the ratio of your Encumbrance to your maximum Encumbrance that determines how much you are slowed by what you are carrying. Thus, carrying 20 units of weight with a Strength of 30 (max: 150) will slow you twice as much as carrying the same 20 units with a Strength of 60 (max: 300). This is one slight advantage of Feather over Fortify Strength. If you can get enough Feather to bring you down to 0 Encumbrance, you will move considerably faster than if you used Fortify Strength to be able to carry the same amount. However, the amount of Feather required to do that is much higher, so this is harder to do.
Encumbrance can be negatively affected by the Burden spell. Enemy spellcasters may use this on you to cause you to be stuck in place while they and their allies attack you. This is a particular hazard for packrats that like to collect every piece of semi-valuable loot they find. You can also use Burden spells on your enemies, but they're much less likely to be effective, because most enemies in the game are not carrying anywhere near their maximum Encumbrance, so it would take a very powerful Burden spell to cause them to be unable to move for long enough to be of any use. Another option is to use a Damage Strength spell. These have the advantage of being permanent, in addition to lowering their melee attack damage, though you may have to cast the spell many times for it to be effective. Drain Strength is easier to cast, but also temporary. A simple Paralyze spell is generally a much more viable alternative to trying to encumber an opponent, and has the added advantage of making them unable to fight back.