Delaney \d(e)-la-ney\ as a girl's name (also used as boy's name Delaney), is pronounced da-LAY-nee. It is of Old French origin, and the meaning of Delaney is "from the alder grove". From "del aunaie". Also possibly (Irish, Gaelic) "offspring of the challenger" or "angel from heaven".
For more information, see also the related name Trelane.