The theory is that there are a lot of people out there that regret missing a previous opportunity, and they aren't about to miss it if it seems about to happen again. If a stock has twice reached $5.00 a share and then dropped to $4.00 straight after that, traders become very wary about the idea of buying anywhere near $5.00 again. The $5.00 jinx becomes well established in everyone's minds and then a fall from that point becomes a self fulfilling prophesy. Whether or not there is any rational reason for the stock to have its price capped at $5.00, enough people are going to start selling their stock at that price that it will only be with great difficulty that the price does pass through.
The name for this phenomenon is "resistance". And if you look at a chart you will see many examples of resistance at work, though admittedly the trouble with humans is that they are very good at seeing patterns even when there is nothing really there. Once you start looking for resistance you will see it everywhere.
"Support" is a lower limit on the price. This is where traders have regrets about missing a great buying opportunity in the past and are determined not to miss it again. That stock that keeps bouncing off $5.00 on the upside might always fall to $4.00. Below $4.00, think traders, the stock is undervalued, above $5.00 the stock is too expensive.
(At this point forget about value in the context of fundamental analysis, I am referring to the fickle opinions of traders here, and this has nothing to do with any item on the balance sheet or income statement.)
So, having missed two great buying opportunities in the past when the stock rocketed from $4.00 to $5.00 there will be a lot of traders waiting for their chance to make this play again. Next time the price hits $4.00 there may be a surge of buying. The stock price has "support" at $4.00.
Support and resistance levels are not inviolate. Once a stock successfully breaks through a resistance level it is said to have made a "breakout". If the breakout occurs on significant volume and looks convincing enough to most people traders will as a group change their mind about valuation, and accept the "new" value. When a stock has broken though a resistance level, that level then becomes a support level.
For a real life example, look at the Dow Jones Industrials as it tried to break through 10,000 in 1998-99. In early March 1999, the Dow hesitated before it reached 10,000, fluctuating all over the place for a while before finally breaking through the 10,000 "barrier". When it did break through it did so in the most convincing manner, rocketing up in a powerful surge to over 11,000 on the 28th of April 1999. Since that time the market has rocked back and forth, getting not much below 10,000 and not much above 11,000, these lines are the new support and resistance.
Of course, the trouble with support and resistance, just like trend lines and every other technical factor is that they only work until they stop working. Most of the time the market is going to stay within trading ranges but eventually it is going to have to get out. If you bet the farm on support or resistance you will one day be in for a real shock.
It is interesting that Alexander Elder, of Trading for a Living fame says that while most amateur traders trade "breakouts", most professionals "fade" them, betting on support and resistance being maintained. Professionals make money more often, but need careful attention to risk management (in the form of stop loss orders) because this technique can lead to rapid losses.
There is a joke told by traders that "support and resistance is the cop of the trading world, it is never around when you need it."