It means that you have four parts of something, and they are all identical in every aspect that matters.
Suppose there are 7 dimes, and someone gives you 4 of them. Each dime they gave you represents a part of the whole amount of dimes, and each of those dimes is equal to the others in size, weight, color, value. They are 4 equal parts of the whole amount of dimes. (The four equal parts don't have to add up to the whole--except when we say the whole is divided into 4 equal parts.)
Usually, we talk about equal parts when we are dividing something into shares. If we have a pizza that four people want to share in such a way that each person gets as much as possible without any fighting, it would usually be divided into four equal parts. Each share would be the same as the others in every aspect that matters. Each of those parts would be 1/4 of the pizza. The "4" in that fraction tells you the number of equal parts. The "1" tells you the number of those parts any one person gets in this scenario.
_____ Each of the words in that phrase "4 equal parts" has its usual dictionary meaning.
