Couch Surfing is a way for people to travel on low budget and also meet people who live in their destination city.
The idea is this:
People register to the site (www.couchsurfing.org) and offer a place to stay for travelers who plan to visit the city where they live.
Travelers also register to the site and search for people who can host them on their trip.
Travelers apply to the hosters and specify the date of their journey, and the hosters decide which traveler(s) they would accept and host in their place.
All of this is 100% free, travelers look for a place to stay, hosters offer a place in their own house, and the match is happening thought the web site.
"Couch Surfing" is today considered a way of life, there are many people who are registered to the site, some are very active, some are not.
In Riga (and also in many citied around the world), there is a long list of people who offer their home for travelers and for free.
More information in the web site: http://www.couchsurfing.org
Specifically in Riga: here