The capping agent (or surfactant) can affect the nanoparticle in many areas including synthesis, surface stabilization, functionalization, and reactivity.
The capping agent has an important role in synthesis. Capping agents and their concentration have an effect on what size nanoparticles nucleate. Also, after nanoparticles nucleate they will grow in size, and the size to which they grow can depend on the capping agent. The capping agent can provide steric bulk at the nanoparticle surface (stabilization) which can prevent agglomeration or further growth.
Also, the capping agent on the nanoparticle surface provides the ability for the nanoparticle + surfactant ensemble to further react with other species, depending on the composition of the capping agent. Here is an excellent paper by S. Laurent:
Magnetic Iron Oxide Nanoparticles: Synthesis, Stabilization, Vectorization,
Physicochemical Characterizations, and Biological Applications
Article Laurent S, Forge D, Port M, Roch A, Robic C, Vander Elst L, ...