The legislative branch is two houses. The House of Representatives and the Senate.
When we are electing a president, the legislative branch exercises democracy because when the people of a specific state vote for someone, majority whens and the number of the Senators and Representatives that state has counts for a vote for that person who’s campaigning. That is how the legislative branch helps in democracy.
(I’m aslo hoping you have some idea of what the legislative branch is, thats why i didnt explain it like you’re 3, like i usually do to answer questions. Hope this helped).