Step-growth Polymerization
In a step-growth reaction, there are no free radicals and therefore, the chain does not have a highly reactive end. Instead, a normal chemical reaction takes place between the functional groups of two monomers and combining into one. Usually there is a side product as well, as shown in Figure 9.6.2, illustrating the step-growth polymerization of nylon 6,6, which results in an $\ce{HCl}$ as a byproduct. In that reaction, two different monomers—adipoyl chloride and hexamethylene diamine— react to form a single molecule. Because each of the monomers has the same functional groups at each ends, the two ends of the new longer molecule can react again with the other type of monomer, resulting in the chain growing "step by step" in both directions.
Just as there exists an incredible variety of monomers available to combine into polymers, there are different chemistries by which monomers are assembled into polymers. Step-growth polymerizations are a common method of combining two or more monomers into polymers. One way of thinking about step growth is through an old children's toy: Tinker Toys.

Figure 9.6.1 Tinker toys consist of connectors and rods. Rods can connect to connectors and vice versa, but rods and rods or connectors and connectors cannot link to one another. With these two pieces, long chains or networks could arise.
If you aren't familiar, tinker toys consist of long poles and connectors which can be assembled into many different architectures. However, the poles cannot be connected to one another, and neither can the connectors. To build a structure out of tinker toys, the poles and connectors must alternate. With just these two simple units, complex structures can be produced, from linear to networked. As with tinker toys, step growth polymerizations consist of two or more monomers which can form bonds with their counterparts but (usually) not each other. The individual monomers can be short like Tinker Toy connectors or long like poles, and they may have two or more functional groups with which they can "connect" to other monomers.

Figure 9.6.2 Step growth reaction of Nylon 6,6. It is called 6,6, because both of the monomers that create it have six carbon atoms.
Figure 9.6.3 shows a generic abstract representation of a step-wise polymerization process. The black circles represent one type of monomer and the white circles represent another kind. They react together step by step to eventually create a long polymer chain.

Figure 9.6.3 An abstract representation of a step-growth polymerization process between two types of monomers