Why are there so many audio hookups on my computer?

They're for different audio products. For the most commonly used ones, in general (but not always), the pink jack is the input jack for a microphone and the green jack is the main line-out jack for extraneous audio devices / control devices such as amps, speakers, or headphones.

The other colors are for more specific / specialized devices, and the jacks included depend on the motherboard the computer has. Two more jacks include the black jack for a rear speaker and the orange jack for a subwoofer.