How much do you know already? Depending on that, I'd advise you to google the definition of a vector or watch some of Walter Lewin's Physics I video lectures at ocw.mit depending on your level of understanding.
The dot product is used often for finding the fraction of a vector quantity that is applicable in a particular direction. Like if you are pushing with a force vector in 3-space (x,y,z), and you want to know the component of that total force that is directed in the horizontal x axis, for example. Or you are calculating the EMF (electromotive force) along a wire in 3-space, resulting from a general electric field distribution....
The main application is finding the "projection" of a vector on another vector or a direction. A variant of that is using the dot product to determine if two vectors or two directions are at right angles. Of course, the angle itself between two directions is determined using the dot product.
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