According to Surname Database the surname Kelley, with the variant spellings of Kelly and Kellie, has three distinct possible origins.
It is an Anglicized form of the Old Gaelic name "O'Ceallaigh". The Gaelic prefix "O" indicates "male descendant of", plus the personal byname "Ceallach" which means "strife" or "contention".
The surname may also be of English origin, from a place called in Devonshire, recorded as "Kelli" in the 1194 Pipe Rolls of the County, and named with the Welsh/Cornish "celli", which means "grove".
The name may also be of Scottish territorial origin from the lands of Kelly near Arbroath, Angus, named with the Gaelic element "coille", which means "wood or grove".