OpenStreetMap is a map of the world, created by people like you and free to use under an open license.
In the web UI, OSM can't be zoomed in far enough to see the names of POIs in reasonably dense areas. I can get around this by going into edit mode, and mobile apps don't have this restriction. But the out-of-the-box experience, for non-insiders just using the web site, doesn't reveal all that OSM has to offer.
In order to make any kind of devices able to visualize the map, the tile server will distribute rasterized tiles, which are easy to process even on a low-powered device. The drawback is that those tiles need to be generated by the server and more importantly stored. A tile of the entire earth zoomed out will not take a lot of storage, but the higher you zoom, the more tiles you need. If you don't put a higher limit to the zoom level ,it will take an exponential amount of storage on the server, which is a problem.
Soon no more! As they will move from pixel based tiles to vector based rendering which will massively speed up load times and allow any zoomlevel you want.