Write a function that finds the intersection of two sets. The function should return a new set containing only elements that appear in both input sets.
Examples:
Input: set1 = {1, 2, 3}, set2 = {2, 3, 4}
Output: {2, 3}
Explanation: Elements 2 and 3 appear in both sets
Input: set1 = {'a', 'b', 'c'}, set2 = {'b', 'c', 'd'}
Output: {'b', 'c'}
Explanation: Characters 'b' and 'c' appear in both sets
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