It’s an Illinois thing. Municipal elections in Illinois have been held in spring for more than 100 years. If they were held in November, they would be drowned in the hubbub surrounding state and national elections.
Nowadays we could avoid this problem by holding municipal elections in November of odd-numbered years. New York does this. However, this wasn’t always possible in the past; until the 1920’s, Chicago wards had two aldermen serving staggered two-year terms, so there were aldermanic elections every year. (Oh joy!) So the only way never to conflict with state elections was to move to spring.
The move to two-round elections required the first round to be held in February so the second round could be held in April. Originally the first round was a partisan primary, since the 1920’s (for Chicago aldermen) and the 1990’s (for the mayor) the first round has been a general election, with the second round a runoff.
The mayor, clerk, treasurer, and all 50 alderman are up for election.