Kitchen sink drama (sometimes known as "kitchen sink realism") is a genre not exclusive to, but better known as coming from British theater, novels, films and teleplays that depicts an ordinary domestic setting, and typically relays a fairly ordinary 'family' story. They tend to be fairly depressing and negative, but are sometimes treated as "serious art", which isn't meant for entertainment.
The term "kitchen sink drama" comes from a painting by John Bratby, the subject of which was in fact a kitchen sink. David Sylvester wrote an article about trends in English art and titled it "The Kitchen Sink" as a reference to Bratby's painting. It was Sylvester's opinion that domestic scenes were becoming popular with painters because they were able to stress the "banality" of everyday life. The term began being associated with a style of drama that showed its viewers a more realistic view of everyday life for the working class.
In kitchen sink drama, conflict generally arises between husband & wife, parent & child, or between siblings. Also applicable are conflicts between the family and others in the community, such as rent or bill collectors and the typical "disapproving family".
These various works are usually set in Northern England, and the characters generally speak in accents and use slang from the area. They showcase working class British people who usually live in rented flats or apartments and frequent pubs. These situations are used to probe and examine socio-political issues & controversies.
The trend, which started in the late 1950s, continues to trickle down into current media, including Coronation Street, the most-watched program on British television (and with which Morrissey, of The Smiths, was fascinated; this eventually led to his repeated references to the genre's main ideas during the 80s with The Smiths and during his solo career in the 90s and today).
American art has a similar genre, known as the "Ash Can School", which examines life in the poorer parts of New York, but that is another node for another day.