The convert rail button will activate a drag-and-drop tool that allows you to convert one type of rail to another (rail -> monorail -> maglev). This tool can be used on rail, depots, stations and waypoints.
Trains you already have running should be sent to the depot and then sold.
Tip: To save time converting a train with lots of orders from one railtype to another, send your train to a depot of the old type and sell it. While the depot window is still open, convert the depot to the new railtype, and the next train you build will have all the orders of your previous train. The depot window must remain open throughout this operation. Note that you can only convert one train at a time using this method, but you may also convert the depot back to the old railtype so you can convert another train using the same depot.
For converting to a compatible railtype (e.g. electrified rail), updating trains is not immediately necessary as steam and diesel trains run perfectly on electrified rails. Electrified trains, however, will not pass over non-electrified tiles.