It depends entirely on your specific system. I’m guessing that you did not build the system, but it doesn’t really matter. Whether a system is custom built, assembled at a small computer shop, or by a large firm, it can be different because there is no universal standard to audio connectors.
In some systems, the front and read jacks are physically connected to the same connector (i.e., they act as a splitter). In other systems, they are connected to different ports on the motherboard. In others still, one or the other may not be connected at all. Vestigial connectors like this are common because generic cases could be used for a variety of models, some of which may have a certain connector be live while others don’t.
In general, when both are connected, as Ian said, the front is usually a stereo connector for headphones while the rear has surround-sound connectors for connecting to a receiver or external speakers.
As Ian suggested, you would have to either check the manual (if available) or simply try them both to find out what the case is for your particular system.
One thing to note however is that you may have multiple audio-adapters and/or devices in your system. For example, my rear audio connectors are from my sound-card while the front jacks connect to the onboard audio adapter. My motherboard also came with a cable to insert in the backplane that can connect to the board and has jacks for S/PDIF, MIDI, and Line-out. To test everything properly, I would need to make sure that something is playing on each device (e.g., both audio devices as well as wave, MIDI, CD, etc.) and that the volume settings are all correct. Otherwise, I could mistake something as not working simply because Windows plays all sounds through the default audio device unless I specifically select another one, or maybe the non-default just happens to be muted and I didn’t notice.