The tiles (single part of the map rendered as images) on OpenStreetMap are refreshed at different rate depending on the zoom level (i.e. zoom 18 might take 1 day to show the "new" data, while zoom 11 might take longer), but your edits are already saved in the database. If you want to be sure, right click where you made the edits and click on "Query features" (if you don't have the website in english, it's the penultimate option in the right-click-menu).right-click-menu).
See also the page on wiki [Slippy Map#OpenStreetMap "Standard" tile server][1]
[1]: https://wiki.openstreetmap.org/wiki/Slippy_Map#OpenStreetMap_.22Standard.22_tile_server