The "audio codec" is a separate chip (a Wolfson WM8731 in your case) which can turn information on digital form into analog information to be amplified/played through a standard sound system with amplifier/speaker/etc.
You'll need to find out how to interface to the audio codec chip from the FPGA (google a datasheet for the chip), and then send it the necessary information to generate you beep. Depending on how advanced the audio chip is, this task can vary rather much in complexity. As it's an educational board, you might be able to find people who've already done something similar, and then build on their experience.
If all you need is a simple beep though, you might also be able to create a simple circuit with a piezo-buzzer or similar yourself - that can be controlled without having to use an audio codec...