The correct answer is C. develops, supports, or explains the main idea of a paragraph
A supporting sentence, as the name itself says, is there to support something. In essays, it supports the main idea within a paragraph, by providing evidence, proof, arguments, quotes, etc. in order to reinforce the main idea.
A is incorrect because transition words are used to do that, and not supporting sentences
B is also incorrect because new ideas are introduced by topic sentences, rather than supporting ones
D is incorrect because this is known as a conclusion, not a supporting sentence