What is it?
This is a little card that you buy which can then be exchanged for unlimited train tickets for the duration of the period you booked it for. So, slow trains and KTX. But not subways. This saves you a fortune if you're doing multiple transfers, or going up to Seoul for the weekend, for example.
All prices in KRW:
KTX from Daegu to Seoul: 33,600 - 55,300
Saemaeul (slower): 30,000 - 34,000
Mugunghwa (slowest train): 17,200 - 20,000
Bus: 17,000 - 27,700
Those are one way trips. Yeeeeeeeeesh. So, a return ticket to Seoul on the KTX will total over 100,000 if I want to travel in style, or 68,000 if I slum it. Ouch.
Now, we get to the Happy Rail Pass. This pass is best used when travelling in a group.
Happy Rail Pass (solo) for 2 days: 87,000
Happy Rail Pass - saver - (solo) for 2 days: 78,300
Edit: I misread the information, unfortunately. The group price is 78,300 per person.
And that is including your return ticket home, and any KTX/slow train travelling you do during that time.
The Happy Rail pass is aimed at visitors travelling within Korea, but it can be used by anyone, including foreigners with ARCs. You need to use a credit card and your passport number when booking, and include the names and passport numbers of your companions if you're putting them on the same pass. Bring your passport with you when you go to the train station. You can use foreign credit cards to book this pass online.
When you get to the station, take your Happy Rail Pass number (you got it when booking) and your passport to the ticket window. Exchange it for your first ticket. The timer starts now. Keep the little card they give you; that is exchanged for all train tickets during this time except subway tickets.
The Happy Rail Pass doesn't guarantee you a seat rather than standing ticket during peak season, so get there well before it's time for the train to go in order to be certain of one. Peak season is summer vacation, Chuseok, lunar new year and Thanksgiving day, year end and beginning of the year.
Book your ticket online here: http://www.korail.com/
(English version of the site is available). Happy Rail passes are under "Travelling".