Yacht Rock is a soft rock genre. Inspired by, or named for, the 2005 Channel 101 series of the same name, the "genre" is mostly 1970s smooth jazz and soft rock singers (almost always male).
Some examples include Kenny Loggins*, Michael McDonald, Christopher Cross, Steely Dan, Toto, and the Doobie Brothers. These artist, and this subgenre of soft rock really peaked in the mid-70s to '80s, and therefore a "restrospective" title. In theory, the "yacht" in yacht rock refers to white, WASP-y yacht owners who would enjoy this music. (Or, for fans of The 40-Year-Old Virgin, big box store managers.) Some songs included references to sailing, some performers dressed as ship captains, and some music videos were set at sea.
Some music journalist have long-accepted this as a Thing, and hipsters (as they are wont to do), quickly latched on. The term is often used to lampoon the genre, but Jimmy Fallon's running gag was a gentle mockery based in reverence. So be prepared either way, and feel free to let those whippersnappers know you remember when that music was NEW.
(Make sure you check out Fallon's videos and peruse the resources I've provided below!)
*Who I sometimes accidentally call Kenny Rogers in my verbal explanations. My apologies!
Yacht Rock, IMDB
Yacht Rock Docks in New York, The New York Observer
Top 10 Yacht Rock Songs Of All Time, IGN
Monday We're Having A Yacht Rock Party Late Night With Jimmy Fallon The Blog
Yacht Rock 2K11! Late Night With Jimmy Fallon The Blog
Yacht Rock, UrbanDictionary.com