A divergence occurs when two markets, a market and a benchmark index, or a market and an indicator move in opposite directions. Common examples include one stock index (e.g., the Dow Industrials) moving higher while another stock index (e.g., the Dow Transports) move lower, or when price makes a new high and a momentum oscillator (like the RSI or stochastics) makes a lower high).
The implication is that by moving in the opposite direction, the indicator (or secondary market or index) is not confirming the price move in the market from which is diverging. Corrections or reversals sometimes result in such circumstances.
Note: Oscillators often produce multiple divergence signals in strongly trending markets before the trend actually reverses; view such signals conservatively.