Oooh. This is a good question. Reminds me of Garnet from Steven Universe. "When two Gems combine, it creates something greater than the sum of their parts."
Steven Universe may be a cartoon but the themes and lessons are honest and true, so! Going off of the two identical phrases, once can infer that the reason a person is greater and different than the sum of their parts is because each individual part compliments the other or makes it stronger. It's the importance of the "connection" between each part that makes the whole greater.
The easiest way to explain it would be with the word "synergy"; the interaction of elements that when combined produce a total effect that is greater than the sum of the individual elements.
Hopefully this helps!