the leaves branch out from the branch like a feather

The illustration at Faldage's link,
http://www.bartleby.com/61/74/P0317400.html
shows a stalk with nine little green blobs attached, four on each side and one at the tip. The blobs are leaflets, not leaves; "leaf" is the word for the entire structure, stalk plus leaflets. Hence the leaf -- the entirety -- has a feather-like structure (a central rib about which numerous appendages are symmetrical).

That particular picture appears to be a locust leaf. If you examine one up-close-and-in-person, there's a small knob where stem joins branch, but no such knob where leaflet joins stem. I assume (but do not know) that that is the technical distinction between leaf and leaflet.