Measuring the colloidal nanoparticles stability by dynamic light scattering
Dynamic light scattering is a sizing technique; that is, it provides an indirect measurement of the size of nanoparticles (details may vary depending on experimental set-up).

However, it's important to note that it doesn't provide a direct measurement of the solid particle, but of its effective size when moving in solution. In other words, it measures the hydrodynamic radius of the nanoparticles - which, by the way, is not a single value but an ensemble average, which you usually measure in statistical fashion.

Now, at the nanoparticle-solution interface, you have several layers of material that is bounded to the surface and will move around with the nanoparticle, contributing to the hydrodynamic radius. In this particular paper, you have a CTAB/C monolayer (at least) which will be more or less tightly bounded to the gold particle, and also counter-ions to provide charge balance and several shells of solvation water (progressively less ordered and more weakly bound as you move away from the particle). It's the size of that whole entity that you measure (indirectly) with DLS.

As you can imagine, reducing the concentration of CTAB/C in the solution will change nanoparticle coverage - and will change the size, shape and strength of the layers surrounding the nanoparticle. As with colloidal systems, when synthesising nanoparticles there's a real concern that they can aggregate and precipitate or otherwise change their properties - which is the reason that you produce them in the presence of an stabiliser such as CTAB/C in the first place. If you look at figure 4, the histograms show hydrodynamic size for DLS measurements in different conditions and you can see they show that this aggregation isn't happening: if it did, you'd see far larger objects moving around in the solution. And as the body of the article explains, the small changes in hydrodynamic radius are probably due to the removal of CTAB/C from the nanoparticle surface, which affects solvation shells and changes the DLS-measured radius.