There are many different kinds of probability density functions, (one of which is the normal distribution, also called the Gauss density). For example, there is the Gamma density, Chi-squared density, Maxwell-Boltzmann density, etc. They have different kinds of shapes and you try to choose one that best represents your data sample. Each different function basically has an "equation" which graphs out the shape of the curve, and various parameters control the shape. The common thing among the various distributions is that the area under the curve = 1. (and is continuous and greater than or equal to zero on all points, but that is less interesting) In normal distribution, for example, it is described by two parameters, the mean and standard deviaton. The mean just shifts the whole thing left or right on the x-axis (horizontal), and the standard deviation controls the shape. The smaller the standard deviation, the steeper and narrower the "hill", and a large standard deviation will produce a wide short "hill". The main concept is that the area under each of the curves equals one. When you want to find probalities, say that it lies between A and B, you need to calculate the area under the curve between A and B.