"Motown" is both a style of music and a label; in fact, no other label (with the possible exception of its grittier '60s brother, Stax) is more identified with the sound it produced. And although Motown started as a straight R&B label and later moved into genres from Psychedelic Soul to New Jack Swing, for the purposes of this discussion we'll be discussing "The Motown Sound" as it's usually understood by fans and historians.
The signature label sound that Berry Gordy created at 2648 West Grand Boulevard in Detroit, Michigan was a pop-soul hybrid he correctly dubbed "The Sound Of Young America." The typical Motown song was a bright, uptempo number done as a 2/4 shuffle or a hard 4/4 beat. Lyrically it dealt almost exclusively with romance, with love won and lost; it also typically featured a very elaborate production which included a sax-heavy, rhythmic brass section, sweet strings, glockenspiel or other bells, and a surprisingly funky bass line, usually provided by the legendary James Jamerson. Solos were generally eschewed in favor of pop songcraft, and singers typically walked the line between hardcore gospel testifying and smooth jazz balladry. (Indeed, most of the "Funk Brothers," the backing band on many Motown songs, were jazz musicians by trade.) Most Motown songs were written on piano and based on a piano riff, although there were occasional ballads that broke the mold (the Temptations' "My Girl").
As the Sixties wore on, soul got grittier and more socially aware, and while the better Motown artists made the transition with spectacular results (Stevie Wonder, Marvin Gaye), others, like the Supremes' Diana Ross, were forced to go pop to compete. The Motown Sound gradually faded, but has never left the public consciousness in America or the UK; in the Eighties, it sparked a mini-revival among MTV bands who'd grown up on the genre.