Sums 3 DC inputs, DC output.
1) The two resistors connecting the inputs are averaging the inputs. Recall that the formula for calculating an average is the sum of all values divided by the number of values (sum/count).
2) The non-inverting amplifier amplifies the signal with a gain equal to the number of values (the same count used in step 1. This cancels out the division done in the averaging step, leaving only the sum of the inputs! In this case, there are 3 inputs, so the amp must have a gain of 3.