A random variable is a variable taking numerical values determined by the outcome of a random phenomenon. The probability distribution of a random variable X tells us what the possible values of X are and how probabilities are assigned to those values.
A random variable X and its distribution can be discrete or continuous.
A discrete random variable has possible values that can be given in an ordered list. The probability distribution assigns each of these values a probability between 0 and 1 such that the sum of all the probabilities is 1. The probability of any event is the sum of the probabilities of all the values that make up the event.
A continuous random variable takes all values in some interval of numbers. A density curve describes the probability distribution of a continuous random variable. The probability of any event is the area under the curve and above the values that make up the event.
Normal distributions are one type of continuous probability distribution.
You can picture a probability distribution by drawing a probability histogram in the discrete case or by graphing the density curve in the continuous case.