A volatility whose magnitude is theoretically set the same across different delta values of an option. The standard Black-Scholes model uses flat volatility for simplification. However, in the real world, kurtosis and directional view of a particular market cause volatility to change over time.
For example, caps (call options on interest rate) are quoted in terms of flat volatilities which represent the implied volatility of a cap when the same volatility is applied to all the caplets forming the cap.
A flat volatility is also referred to as a fixed volatility.
