Support (Support Level)
  
Stocks bounce around day-to-day. Even shares that are generally moving sideways never just hold at one particular price. They rise for a bit, then fall for a bit, then back up...back down...etc. This works because, as a stock falls, it gets more attractive to buyers. The price is lower, so more people are willing to buy it.
Eventually, it reaches a level that convinces a large group of people to move into the stock. That buying interest sends the stock higher. People continue to buy until it gets too expensive. At that point, buyers are limited and some of the holders start selling the stock to lock in profits. That selling pushes the stock lower...until, of course, it gets cheap again and buyers reemerge.
The points where the buyers come back into the stock, the price levels that the shares never seem to drop below...that area is known as support. It's like a floor underneath the stock.
Shares drift up from $12 to $15. At $15, the stock seems too expensive for most people. Holders start to sell. It falls back down toward $12. At around $12, people look at it and say, "Hey, that stock's gotten pretty cheap; I don't mind taking a flier on that." They start buying again.
That $12 level is called support. The more times it gets close to $12 and turns back toward the upside, the stronger the support is said to be.
Technical traders look for support levels. In its simplest form, this involves drawing horizontal lines across a chart at points where the stock has reversed course from a downward move, back to the upside. These lines define support. On a more advanced level, there are mathematical techniques to determine more precise support levels.