As far as I understand it, the (Boeing) FPV is derived mostly from IRS output, thus allowing an instantaneous display of Flight Path Angle and drift information.
The FPV consists of a small aircraft symbol which moves over the 'attitude indicator' part of the PFD. If you were stationary on the ground, it would be on the horizon line and centered in the display. It shows the actual angle of climb/descent referenced to the Earth's surface.
If you took of in a 15Kt crosswind and rotated to 20degs pitch angle, you would see the 'Airplane Symbol' (pitch bar/wing bar) at the 20deg mark. Underneath it (normally!) and to one side would be the FPV, indicating maybe 13degs FPA and a bit of drift.
When you next levelled off, you would see the pitch bar at an attitude commensurate with your configuration (speed, weight, flap, etc.) but the FPV would be on the horizon line, indicating level flight.
When you descended on an ILS (assuming you followed the glidepath exactly), the pitch bar would move around quite a bit during flap/gear extension and speed changes but the FPV would stay at 3degs ND (or whatever).
That's the basics.
I find the FPV a very useful bit of kit and here's some reasons why:
It allows you, at a glance, to assess the performance of the aircraft. If the FPV is in the blue part of the AI, you are definitely going up. Vice-versa when you are 'in the brown'.
If you are unlucky enough to have a bad windshear encounter, the first instrument to warn you will be the FPV (assuming the PWS hasn't gone off) as it assumes an unusual position (drops away or rushes up). This is because your other cues (altitude, ROD, airspeed) have significant lag before they show the true picture. It also provides, as mentioned in the previous paragraph, an instant answer to "are we going up or down?"
It is a very good tool on non-precision approaches, especially once you have gone visual, or at night. Many airfields have no (visual) slope guidance and quick glances at the FPV will help stop deviations early.
You can set FPA on the MCP and get a sort of 'mini flight director' which brackets the place where you want the FPV to be to achieve the desired FPA. This is useful if you want a 3deg slope as the AI graduations are in 2.5deg increments...
Height keeping when flying S&L becomes simply a task of keeping the FPV on the horizon. You also become much more accurate as the other instruments (including the FD) only steer you back once you have made a deviation. The FPV registers the smallest trend immediately.
A 'fun' use is with crosswind landings. If you take a peek at the FPV every now-and-then (assuming use of the 'wing down' method), when you are fully aligned with the runway the FPV will be in the centre.
This is all from using the 777 FPV. I am told that the 737NG one is the same but I don't know if this is true...
Happy vectoring!