Vector tiles make huge maps fast while offering full design flexibility. They are the vector data equivalent of image tiles for web mapping, applying the strengths of tiling – developed for caching, scaling and serving map imagery rapidly – to vector data.
Traditionally, maps are created from image tiles. But vector tiles contain vector data instead of the rendered image. They contain geometries and metadata – like road names, place names, house numbers – in a compact, structured format.
Having the Open Street Map data available as vector tiles, for example, makes it possible for you to design your own map exactly how you want it.
Mapbox Studio is the best place to start for designing basemaps. It's based on Open Street Map and vector tiles.