Connelly is a name you will find much more often as a last name (Jennifer Connelly, for instance) rather than a baby name, but lately it has been used for both boys and girls, likely because it fits in with such names as Connor, Colin, Cassidy, Kennedy, Delaney and Ainsley. For girls specifically, it can be seen as a modern update to Colleen.
Since it originated as a surname, Ó Conghalaigh, it is considered unisex. Some experts claim Connelly (KON-ell-ee) is an Irish Gaelic name meaning "valiant hound/wolf," from con and gal, while others say it means "love," from the word conal. I believe neither of these translations are modern. If we take a look at Connor, which means "dog/wolf lover" from Conchobhar, and Conall, which means "strong wolf," and Conley, which means "chaste fire," then the likely meaning of Connelly is "valiant wolf."
As a last name, there are just under 30,000 people in the U.S. with this name. As a first name, there are only about 180, and it seems to be split fairly between boys and girls, only being used from about 1991. Since then there have been about 74 girls and 74 boys, making it a very rare baby name.