maxzoom
maxzoom is the highest zoom level a tileset was generated for. It appears in tileset metadata, in a style JSON’s source declaration, and on individual style layers, and it means something slightly different in each place.
maxzoom on a source
On a source, maxzoom states the highest zoom level at which real tiles exist. For most OpenMapTiles tilesets that is 14.
This does not mean the map stops at zoom 14. Above the source maxzoom the renderer keeps using the tiles from the maxzoom level and scales them up, which is called overzooming. With vector tiles the result still looks sharp, because the geometry is scaled rather than the pixels, so zoom 18 draws crisp roads from zoom 14 data.
Generating tiles beyond 14 is worth it only in specific cases, such as indoor or cadastral data whose fine detail cannot be recovered by overzooming. The number of tiles quadruples at every level, and vector data overzooms well enough that the extra storage usually buys very little.
minzoom and maxzoom on a layer
On a style layer the pair sets the zoom range in which that layer is drawn. This is how a style shows motorways at low zoom levels and adds residential streets only at high zoom levels, and how label density is kept under control.
The two uses interact: a style layer with a maxzoom of 12 is hidden from zoom 12 upwards, no matter how high the source’s maxzoom is.