Huygens' Principle, simply stated, is the following:
Every point on a wave can be considered as a source of tiny wavelets that spread out in the forward direction at the speed of the wave itself. The new wave front is the envelop of all the wavelets -- that is, the tangent to all of them. (Douglas A. Giancoli, Physics)
Huygen's principle, developed by Dutch physicist Christiaan Huygens (1629-1695) is used to determine the future position of a wave front when its past position is known.
For example, consider a wave front from A to B, traveling away from point S at velocity v. This wave is assumed to be isotropic, meaning that the wave is moving away from S at the same speed in all directions. To find the position of the wave after t seconds, we can draw tiny circles, or wavelets from every point (in reality, as many as possible) with radius vt. The tangent to these wavelets is the position of the wave after t seconds. Huygen's principle is very important for determining the position of a given wave, especially after the wave diffracts after hitting an obstacle.