Stan, so far, has the best explanation. Swing is a style of phrasing and playing.
Two eighth notes fit into an eighth note triplet frame. Four eighth note triplets are
counted "one and uh, two and uh, three and uh, four and uh"

The first of the two eighth notes in a swing phrase are treated as:
"one and" and the second of the two eighth notes is the "uh".

In others words, a triplet frame is imposed on two eighth notes where the
first two notes of the triplet are the equivalent of the first eighth note and
the third note of the triplet is on the second eighth note.

Swing players are actually thinking in 12/8 time when they play in 4/4.

Jazz and swing players are unconsciously thinking fast triplets when they play
standard eighth note lines.

There is a difference between a "swing band" such as found in the forties and
a "jazz band" which by definition relies on improvisation. A "swing band" can be a "jazz band" but the reverse is not always true. Glenn MIller was a swing band but not a jazz band. The same can be said for Kay Kayser, Harry James (except when he took an improvised solo), Lawrence Welk, Guy Lombardo and others that you could dance to but not feature swing artists. Paul Whiteman referred to his outfit as a jazz band but in fact he incorporated jazz musicians such as Bix Beiderbecke, Eddie Lang, Joe Venuti and others into his written arrangements, many by done by Ferde Grofe who composed the "Grand Canyon Suite". The swing bands of the forties accompanied the standard box step of the fox trot and some jitterbug styles.
Some of these dances were known as the "businessman's bounce" employed on hotel dance floors.

There is nothing mystical about swing. It has its antecedents in African music
that occurs in African drum patterns that are in 12/8 time. From these, the blues was transplanted to the New World, and jazz rhythms and ultimately in the Forties,
swing patterns. I think you'd be hard put to say that New Orleans jazz of the Twenties would fall under the classification of "swing" but this doesn't mean that the impelling African-esque rhythms didn't prevail and were suitable for dancing.

The Nineteen Thirties brought to prominence jazz swing bands such as Count Basie,
Duke Ellington, Fletcher Henderson and others that featured improvised solos.
There is also Southwestern Swing introduced by Milton Brown and the Brownies,
Bob Wills and the Texas Playboys and other similar bands that featured steel guitar in lieu of a trumpet or sax section.

The swing elements can be found in contemporary Chicago style blues.

Bebop incorporated swing in its intricacies and the phrasing is felt in Parker and Coltrane, Monk and Powell, and earlier influences such as Lester Young and Jimmy Dorsey (who influenced Bird).

Jazz vocalists employ swing phrasing as well.

The style is distinctly American with African roots as can be said for all of us,
genetically.