This is how my professor explained convergent or linear.
If you want to build up a C16 carbon skeleton (that means a carbon skeleton 10 carbons long in case you aren't familiar with that notation):
Convergent:
C2 + C2 = C4
C4 + C4 = C8
C8 + C8 = C16
Linear:
C2 + C2 = C4
C4 + C2 = C6
C6 + C2 = C8
C8 + C2 = C10
C10 + C2 = C12
C12 + C2 = C14
C14 + C2 = C16
Mind you, this is a highly, highly simplified example, but it should help illustrate the idea. You may separately build up two different C4 skeletons and then combine them, instead of slowly building up the chain, bit by bit.