When the Kohanim washed their hands and feet in the Beis HaMikdosh they did not have anyone to help.
Why then do the Kohanim need others to wash their hands when they go up to bless the people?
Why do the others have to be Leviim if available?
It's based on the Zohar Nasso 146b and is noted as an old minhag in both Ashkenaz and Sefarad by the Beit Yosef (OC 128). In the Shulchan Aruch he codifies this practice in OC 128:6.
It seems the reasoning in the Zohar is that the Kohanim need to somehow up their kedusha level by washing as a preparation for the blessing, and by having a Levi, who has his own type of kedusha (based on a pasuk the Zohar quotes וקדשת את הלוים; I can't find this pasuk in Tanakh but the Zohar quotes it in a number of other places as well) do the washing, it is better able to add to the kedusha of the Kohen. (If you didn't really understand that don't worry: I didn't really either.)
The question can also be asked that even in the times of the מקדש the cohanim were duchaning when they went home. So did the Levi in his hometown wash the kohen's hand? From the pasuk in bamidbar יח-ב we see that the Levi had the privilege of helping in the avodah and the pasuk uses the word "to serve you " so perhaps this also went outside the mikdash if the Kohen is doing his service of Hashem vis-à-vis KO sivorchu...
[This answer seems to be based on the reading of the Torah Temimah, Numbers 18:2]