To change what you see, you need to edit the underlying data.
To change the data, you need to use an editor.
Use on openstreetmap.org
You hold the copyright for the data which you add to OpenStreetMap.
OpenStreetMap is licenced under the
Open Database License (ODbL).
One option is the map on OpenStreetMap.org
Other applications like OSMAND provide offline maps for Android, and iOS devices
OpenStreetMap contributors provided essential maps to Search and Rescue and Relief teams responding to the Haiti earthquake.