Below is a direct screenshot from my save file for quick reference:



The compass took me quite a long time to get used to, but here's how I understand it...

As one can expect, the N, S, E, and W markers on the bottom represent the cardinal directions, north south, east, and west, respectively. The markers will move around depending on the direction you're facing; if, for example, N is in front of you, start walking forward, and you will be heading northward. The in-game map that is featured in your Pip-Boy is fixed north: so "up" is always north, "down" is always south, "left" is always west, and "right" is always east, regardless of what direction you're facing.

The icons on the top part of the compass represent major locations (such as towns, landmarks, and prominent buildings). Icons that look "punched out" represent nearby locations that you have not yet discovered, while icons that look "filled in" represent nearby locations that you have visited before.

These icons will appear when you are relatively near the locations they represent. As you get closer to a particular location, its corresponding icon will gradually increase in size; if the location is a waypoint or quest objective, you will see a number no greater than 99 appear above the icon. This indicates approximately how many paces or so you are from the location. At times, there may be an arrow pointing upwards or downwards, especially when a waypoint or quest objective is indoors from the greater Commonwealth area. If there is no arrow present, this means you are at the "same level" as the objective - naturally, if the arrow is pointing upwards, it means the objective is "above" you, and if it's pointing downwards, the objective is "below" you. This is all helpful information when it comes to pinpointing exactly where your next objective is, such as at a specific terminal or doorway.

If the objective for a quest requires you going into another area that is accessible via a loading screen, an icon in the shape of a door will appear on the compass, indicating that, if you're out in the Commonwealth, the objective is within a more specific location indoors.

Finally, enemies will also appear on the compass. In my understanding, enemy icons will only display when they "spot" you. This means that enemies that are nearby but have not noticed you will not appear on the compass, and enemies that you have escaped and have gone too far from will disappear from the compass. Like with other icons, though, enemy icons, indicated as red squares, will move around the compass in accordance to their proximity to you; you can use this in tandem with the V.A.T.S. to pinpoint enemies you might not see immediately, or are farther away but within sight.