Branches in an organic compound refers to those carbon atoms or chain of carbon atoms that are attached to the parent carbon chain but are not included in it to decide the word root.
Thus,
∙ propane has no chain;
∙ 3-methylpent-2-ene has one as there is one susbtituent, i.e., one alkyl group;
∙ 2,2,3-trimethylpentane has three branches as there are three substituents, i.e., three alkyl groups.