Stack

The term stack in World of Warcraft generally refers to two different things:

A grouped number of the same items which take up only one bag, bank, or equip slot.
The ability of ability, buff, debuff, power, or spell effects to remain active at the same time. If they can work together, they can "stack".

Both have numbers in the lower right corner to indicate how many times they have "stacked".

Many items, particulary reagents, can be "stacked" in your inventory. This just means that more than one of an item can be represented by a single icon in a single slot in your inventory. The icon will then have a number appear in the lower-right corner to show how many of that item you have.
Items can be divided/unstacked by SHIFT+CLICKing the icon in the inventory.
Items can also be restacked by dragging one icon onto the other. If they can't stack, they will simply swap places in your inventory.
Stack sizes vary depending on the item. Common sizes are 5, 10, 20, and 200.
Many items, particularly large items, can't be stacked — items such as weapons, armor, and shields, for example.

"Stacking" spells can greatly enhance your character, but most spells and effects that are similar to each other cannot affect you at the same time, so it is said that the spells don't stack. For example, if you cast a spell on another player that slows them down by 50%, if you cast it on them again while it's still in effect, it won't slow them down the remaining 50%, or even an extra 25% (50% of 50% is 25%).
Some spells and effects ARE stackable, however. Many poisons used by Rogues can be stacked, for example. So, if a Rogue poisons you for -10 hit points per second, then hits you with the same poison, you will lose 20 HP/sec. until the first wears off, then you'll go back to 10 HP/sec.