Breakbeat (sometimes breakbeats or breaks) is a term used to describe a collection of sub-genres of electronic music, usually characterized by the use of a non-straightened 4/4 drum pattern (as opposed to the steady beat of house or trance). These rhythms may be characterised by their intensive use of syncopation and polyrhythms.
In the late 1970s and early 1980s, hip-hop DJs (starting with Kool DJ Herc) began using several breaks (the part of a funk or jazz song in which the music "breaks" to let the rhythm section play unaccompanied) in a row to use as the rhythmic basis for hip-hop songs. Kool DJ Herc's breakbeat style was to play the same record on two turntables and play the break repeatedly by alternating between the two records (letting one play while spinning the second record back to the beginning of the break). This style was copied and improved upon by early hip hop DJs Afrika Bambaataa and Grand Wizard Theodore. This style was extremely popular in clubs and dance halls because the extended breakbeat was the perfect backdrop for breakdancers to show their skills.
The Amen Break, a drum break from The Winston's song "Amen, Brother" is widely regarded as the most used break ever. This break was first used on "King of the Beats" by Mantronix, and has since been used in thousands of songs. Other popular breaks are from James Brown's "Funky Drummer" and "Give it Up or Turnit a Loose", The Incredible Bongo Band's "Apache", and Lyn Collins' "Think (About It)".
In the early 1990s, acid house artists and producers started using breakbeat samples in their music to create breakbeat hardcore, also known as rave music. The hardcore scene then diverged into sub-genres like jungle and drum and bass, which generally had a darker sound and focused more on complex sampled drum patterns. A good example of this is Goldie's album 'Timeless'.
In 1992 a new style called "jungalistic hardcore" emerged, and for many ravers it was too funky to dance to. Josh Lawford of Ravescene prophesied that the breakbeat was "the death-knell of rave"  because the ever changing drumbeat patterns of breakbeat music didn't allow for the same zoned out, trance-like state that the standard, steady 4/4 beats of rave enabled.
In recent times, the term breakbeat has become synonymous with the many genres of breaks music which have become popular within the global dance music scene, including big beat, nu skool breaks and progressive breaks. DJs from a variety of genres, including house and techno, work breaks tracks into their sets. This may occur because the tempo of breaks tracks (ranging from 110 to 150 beats per minute) means they can be readily mixed with these genres, whereas the comparatively fast speed of jungle and drum and bass (160-180 bpm) may have restricted the utility of these subgenres to DJs playing slower-tempo music.
In the present day, breakbeats can be heard constantly in every day life. Breakbeats are used in many hip hop, rap, jungle, and hardcore songs, and can also be heard in other music, from popular music to background music in car and jean commercials on the radio or TV. 
With the advent of digital sampling and music editing on the computer, breakbeats have become much easier to create and use. Now, instead of cutting and splicing tape sections or constantly backspinning 2 records at the same time, a computer program can be used to cut, paste, and loop breakbeats endlessly. Digital effects like filters, reverb, reversing, time stretching, and pitch shifting can be added to the beat, and even to individual sounds by themselves. Individual instruments from within a breakbeat can be sampled one by one and combined with others, to build new breakbeat patterns from the ground up. The Prodigy, a popular group, uses digitally sampled and chopped breakbeats in many of their songs. The advantage of sampled breakbeats over a drum machine is that the sampled breakbeats sound like a real live drummer is playing them, which, of course, was initially true. 
With the rise in popularity of breakbeat music and the advent of digital samplers, enterprising companies started selling "breakbeat packages" for the express purpose of helping artists create breakbeats. A breakbeat kit CD would contain many breakbeat samples from different songs and artists, often without the artist's permission or even knowledge. One example of this is the Amen break. The original song is by The Winstons, who hold the copyright. However, a company named Zero G released a "jungle construction kit" containing an exact copy of the Amen break, slightly sped up, to which Zero G has a copyright. The Winstons have not received any royalties for use of the Amen break.
Breakbeat (or funky breakbeat) may also refer to the music of bands who play funk and soul music with an emphasis on the elements that became popular in hip-hop and later breaks-based music. This sound is characterized by slower tempos (80-110 bpm) and organic, "human" rhythms. It is sometimes differentiated by the term "broken beat".