Suppose A has 2, B has 2 and C has 3 possible values. Their Joint Probability Distribution will contain 2x2x3=12 values.
We can condition the values by setting a variable to a certain value.
We can also marginalize the values to a certain variable and check the distribution of this single variable.
A factor \phi is a function that takes values for A, B and C and returns a real value.
The arguments that the factor takes are called the scope of the factor.
Both normalized and unnormalized measures are factors. But the scope of each can change.
CPD (Conditional Probability Distribution) is another example of a factor.