What exactly does Base Texture Resolution change when creating terrain?
Beyond a certain distance from the camera, the splat mapping shader is no longer used to render terrain sections. Instead, the "base texture" is used, which is a single large texture which approximates the entire terrain's splat map. As a result it's a much lower resolution in proportion to the area it covers, but because it's just one texture, it's much less costly to render.
Because it's only used beyond a certain distance, the idea is that the transition between the nearer splatmapped sections and the further basemapped sections isn't noticeable. The "base map resolution" setting is simply the resolution of this single large texture.
You can see this effect in full by turning down the 'base map distance' setting to zero, which makes the entire terrain render using just the basemap - then you'll see what I mean!