More sophisticated GPS units can display maps and log information from external sensors
We've already looked at the basic GPS functions that pretty much every receiver will have. Here are some others that you may encounter.
Altimeter
While four good satellite fixes can give an indication of altitude, the maths involved (and the differences in the height between two positions on a single bike ride compared to the distance between the trail and the satellites) mean that it's a considerably less accurate and reliable reading than your position. A more accurate reading can be had from a barometric altimeter that use air pressure, and these are sometimes built in to GPS receivers. The downside of this is that they need regular calibration, setting the device at a known altitude or barometric pressure.
Compass
Nearly all GPS receivers include a "compass" display that shows the direction in which you are heading. This is derived from historical position data - the unit knows where you are now and it knows where you were a few seconds ago, so it can tell you which way you're heading. Stand still, though, and it can't do that. To fill in this gap in functionality, some GPS units include a separate electromagnetic "fluxgate" compass in order to give directions or let you take bearings while stationary.
Maps
Some sort of built-in map display is an increasingly common GPS feature. Typically, you'll get a "basemap" pre-installed that includes towns and major roads, with the option to add extra, more detailed maps. Note that even units that can't display maps tend to have a "map" screen that shows your track and any waypoints that you've marked. If you've got onboard mapping, the map page shows your position on the map along with any relevant data related to your trip along the top of the page. You'll be able to configure the display in various ways - whether you want North at the top at all times, or your direction of travel at the top, for example. You'll also be able to zoom in and out and (depending on the map data used) set the level of detail displayed - less detail will display more quickly but will be (surprise!) less detailed.
External sensors
GPS receivers designed specifically for bikes, for example Garmin's Edge series, have optional additional sensors that let them gather and log information beyond that which can be derived from orbiting satellites. Heart rate is an obvious one for training purposes, with a chest strap sending signals to the receiver so it can display current and average heart rates alongside all the other information. Some models can also communicate with power-measuring hubs and cadence sensors, leaving you with vast swathes of data about your ride.