So here's the scoop: audio is all about voltage on wires. There are essentially 3 different voltage ranges used in audio gear: microphone level signals, line level signals, and speaker outputs. On most computers, a line level output and a headphone jack are electrically the same thing. The only difference is the purpose of the jack.
Line level signals have a nominal voltage of around 0.3 volts.
Microphones only generate a few millivolts. That's why you can't plug a microphone directly in to a speaker. You need a lot more amplification to make a mic work.
Speakers need a lot more voltage. The typical home computer speaker system will range from 1 watt all the way up to 100 watts. 1 watt at 8 ohms is around 2.8 volts. 100 watts is 40 volts. (Wall current is 120 volts. This would put out 1800 watts if plugged in to a standard 8 ohm speaker.)
Also, many new computers can separate out the front panel headphone jack in to a separate audio source, so you can use the front panel for voice chat and use the speakers for music or video game sound at the same time.
Finally, the red microphone port is only for microphones. Plugging a line level source in to the mic jack will usually result in a lot of distortion and noise. Use the blue jack if you want to record from another audio device: another computer, a radio, a synthesizer, etc.
The thing is, most computers don't have built in power amplifiers, so you need powered speakers. Fortunately, all "computer" speakers these days have built in amplifiers. Likewise, the audio jacks these days can all handle a wide range of impedances, so there is no real distinction between the headphone and green line out jack, except that the headphone jack on the front may be used independently from the one in the back (if your computer supports it.)