Housing Development Board, basically government housing. 86% of the population live there. There older ones are a bit basic, however the newer ones are perfectly acceptable, they just lack the pool/gym/tennis court that you'll find in the private condos.
There is no stigma attached to living in an HDB, most people buy their own and the estates are clean, safe and well maintained. They are not comparable to "the projects" or a council estate.
Some HDBs are provided for rental by the government to cater to people who can't afford to buy, stay away from these. You aren't eligible as a foreigner anyway.
HDB InfoWEB : Homepage