Capital appreciation is an increase in the value of an owned stock. Capital Appreciation occurs when the market price of a stock you own increases.
For more information on stock prices, see "Why Does the Price of a Stock Change?"
Until you decide to sell the shares, you have what is called Unrealized Gains on Capital Appreciation. Something to be wary of: having unrealized gains can be summed up with the old English proverb, "don't count your chickens before they hatch."
As soon as you do sell them, your profit becomes known as Realized Gains on Capital Appreciation. Of course, as long as you have Unrealized Gain, your profits are fully dependent on the market price of the stock in question — a drop in market value would result in Unrealized Losses, and selling those shares would give you Realized Losses.
Once gains or losses are realized through the selling of previously owned shares, the tax implications of the sale become realized as well. If stocks are held without being sold, unrealized gains can avoid taxation for the time being. The taxes due on such a sale are generally going to be long-term capital gains taxes (if held for more than one year), which are generally taxed at a lower rate than income taxes.