When mutual funds investing in stocks throughout the year buy and sell different companies, they generate profitable trades (hopefully) that add up to "realized" taxable gains. Investors in those mutual funds receive a form 1099 at the end of each year detailing how much their share of those taxable gains turned out to be. This information goes on our tax returns and we pay taxes accordingly.
However, a fund might have invested in, say, Apple (AAPL) and never sold it. The stock has quintupled in value, but because it was never sold by the mutual fund, that gain is known as "unrealized" profit and no annual gain had to be reported.