Illustrated Glossary of Organic Chemistry

Branched: A molecule or polymer with a nonlinear backbone. Branches sprout from one or more atoms of the main skeleton (or from monomers along the chain of a polymer).

2,2-Dimethylhexane is a branched hydrocarbon.
Octane is a linear hydrocarbon. Each carbon of the
 molecular skeleton is bonded to (at most) two other carbons.

Amylopectin is a branched α-D-glucopyranose biopolymer.   
Amylose is a linear α-D-glucopyranose biopolymer.
Branches sprout from glucopyranose carbon 6 approximately

every 25th monomer along the glucopyranose backbone.