The Sharpe Ratio is defined as the expected excess return over the risk-free rate, all divided by the standard deviation of the excess return.
That all might sound pretty complicated, but it really is pretty simple once you understand what everything means.
expected excess return over the risk-free rate: This is simply the expected profit over that which you would receive from an investment with zero risk; usually estimated by the Treasury yield. This is the E|Ra-Rb| above. E stands for expected, Ra is the return for whatever is being calculated, and Rb is the return from investing in a risk-free asset.
standard deviation of the excess return: A standard deviation is a measure of volatility; it measures how much something moves from its average value. So, the "standard deviation of the excess return" is the amount that the excess return (expected profit minus profit from a risk-free asset) will vary. It is basically a measure of "average volatility."
Altogether, the Sharpe ratio is the expected return taking into account the riskiness of the strategy; a.k.a the risk-adjusted return. This metric is widely used in determining whether traders should use a strategy, or choose another one with a better risk-adjusted return profile.