It's mostly about what power & configuration your speakers need. If you don't have a sound card & are only using onboard sound (what you've pictured) Your speakers will always connect through here (bar a few exceptions like usb headphones),
There is 2 channels per port or plug and each channel has 2 wires/contacts.
If your speakers are 2 channel (left & right) theyll plug in the green one.
If your speakers are 5.1 channel as above (left, right, center, sub, rear left, rear right) theyll plug into green, orange, black ones
You could buy a 5.1 and set it up like in this picture;http://ask.creative.com/wwimages/audio_int/dvd_configure_spks.jpg
Note that a sound card is pictured but the colours and theory is the same.
You would have to configure your Windows to output 5.1 sound within Control Panel -> Sound, or your onboard sound control panel.
If your speakers require power theyll have a plug that comes with them to plug them into the wall, if not - no plug. Generally powered ones are louder as they have a built in amplifier.