The phrase "doing business as" (abbreviated DBA or d/b/a) is a legal term, meaning that the name of the business or operation does not include the legal name of its proprietor, the names of all partners, or the official registered name of the limited partnership or corporation that owns it.
In the United Kingdom the phrase trading as is used. This is abbreviated to t/a. In several US states, such names are also referred to as fictitious business names or assumed business names.
The distinction between an actual and a "fictitious" name is important because businesses with "fictitious" names give no obvious indication of the entity that is legally responsible for their operation. Therefore, for consumer protection purposes, most jurisdictions require businesses operating with fictitious names to file a DBA statement. This also reduces the possibility of two local businesses operating under the same name. Note, though, that this is not a replacement for obtaining a trademark. A DBA filing carries no legal weight in instances where a trademark would be necessary.
DBA statements are often necessary with a franchise, where the franchisee may be something like The Big Fast Food Restaurant Company, Inc., but business is done under the brand name the public would recognize, such as Super-Burger (the franchiser). The legal name of the franchise may then be something like "The Big Fast Food Restaurant Company, Inc., d/b/a Super-Burger".
Another example would be someone named Michael Albert opening a retail store. If he calls the store "Albert's House of Junk" it does not require any paperwork. If he calls the store "Junkworld USA", and his state requires it, he needs to file a DBA statement.
Notably in California and also in other areas, filing a DBA statement also requires that a notice of the fictitious name be published in local newspapers for some set period of time to inform the public of the owner's intent to operate under an assumed name.