Surprised you weren't able to find this one yourself ...it's a rather common Irish surname and is pretty well documented...
More often, it's spelt Connolly and can derive from a number of anglicized Gaelic names basically derived from the same root. Ó Conghalaigh comes from the Irish word conghal, and means 'fierce as a wolf' or generally 'valorous'.
The Connolly’s were an ancient sept of Connacht who in time separated and dispersed into three distinct families. They are still mainly based around the counties of Cork, Meath and Monaghan, where they were one of the 'Four Tribes of Tara' (Ireland's royal high-kingship location).
Families with the Connelly spelling may be more often from Connacht (Co. Monaghan is in Ulster, but on the border of Connacht in Ireland's west) where the English version is now spelt 'Connelly' (quite possibly the source of your surname).
The name also arose as Ó Coingheallaigh is West Cork and in Ulster. Any names with ‘con’ usually derives from Old Irish for ‘wolf’ or ‘hound’.