This refrain is used to describe a situation where the total of all the individual parts is less than the total of all of those parts working together.
One of these machines can pull 1000 pounds; individually, three of them can pull a total of 3000 pounds. But if you put the three of them together, they can pull 5000 pounds! So, the whole is 5000 pounds even though the sum of the parts is only 3000!
Jim and Mary each would need a day to finish the project. But if you put them together, they can finish it in a couple of hours, less than half the time! The whole is always greater than the sum of the parts.