A distribution is a description of the population from which samples are taken. We know that most physical phenomena vary from one item to the next. We can use descriptive statistics like range and standard deviation to summarize how data varies. The distribution takes this concept one step further.
A distribution can be thought of as the theoretical concept underlying a histogram. Suppose we had the following histogram of a set of observations:
We can get a better picture of the population this data comes from by taking more observations and increasing the resolution of the histogram by decreasing the range widths:
If we continue this process of taking more data and decreasing the width of our histogram ranges, we are moving in the direction of a distribution, which represents the entire population.
With a distribution, we have an infinite number of "bars" in our "histogram," so we don't talk about the probability of a single value occurring in a sample, but we talk about the probability of an observation being within a particular range of values.
To calculate the probability that an observation will fall in a particular range, we calculate the area under the distribution curve. That is usually done with tables or Excel spreadsheet functions for the particular distribution in question.