Trance emerged as a form of electronic dance music around 1990, with the advent of music that was essentially techno or house, but had simplified percussion, extreme repetition, and other hypnotic effects such as sustained chords and long echoes. Trance generally has no "bump" in its percussion or "groove" in its basslines -- that is, the hi-hats and the bass in the kick drum are generally de-emphasized as compared to house or techno, and the basslines tend to consist of flat tones, with no modulation, confined to a small range of notes. Trance tempos are generally a little faster than techno, but can vary considerably. Additional info: Trance Production section of the Trance article on Wikipedia.
In trance's early years (1990-1992), it wasn't always clear whether a track was just "trancey" techno (or even beat-laden "ambient" or "deep" house), or was actually an example of what would later be called simply "trance". Consequently, on Discogs, such music might be tagged as (for example) both Trance and Techno. Example artists in this category and time period include The Shamen, Psychick Warriors Ov Gaia, The Irresistible Force, and Speedy J. From the New Beat scene, Age of Love's 1990 self-titled hit single is sometimes pointed to as the earliest "pure" trance track. Similarly, some tracks from the Acid House era, such as original versions of The KLF's "What Time Is Love?" (issued in sleeves that say "Pure Trance") were called house or acid house at the time, but are retroactively considered by some to be trance or proto-trance.
The first wave of what many now consider to be "classic" trance peaked in 1992 and waned in 1994, and was dominated by producers and labels from Germany and the UK. Key labels include Eye Q/Harthouse, Rising High, FAX, ESP, and MFS. Hits include Jam & Spoon "Stella", Jaydee "Plastic Dreams", Sequential "Prophet", Transform "Transformation", Cygnus X "Superstring". Other artists of note from this wave include Sven Väth, Cosmic Baby, The Drum Club, The Sabres of Paradise, Horizon 222, Biosphere, Lumukanda, James Bernard, and Oliver Lieb. On Discogs, this music is generally tagged as just Trance.
In the mid-1990s, although it wasn't new, harder-edged, faster, more aggressive sounding trance (Hard Trance, Acid Trance) became more popular than the mellower, more tonal classic sound. Similarly, it was in the mid-1990s that busier, more psychedelic/ear-candy-laden forms of trance became the norm rather than the exception. On Discogs, this music is generally tagged according to which style it is Goa Trance, Progressive Trance, and Psy-Trance), but plain old Trance can be used if the specific variety isn't known. When these styles became more popular, the more basic, classic sound became marginalized, and it did not really re-emerge until the early 2000s, when classic trance-infused techno/tech-house (sometimes called Neo-Trance) became popular. This newer sound is generally tagged with Trance, along with whatever other style applies, indicating it has elements of both.
Meanwhile, the mid and late 1990s also saw commercial, "clubby" forms of trance or trance/house hybrids become very popular, especially in Europe. These tracks often include vocals, overt melodies, and traditional A-A-B-A song structures, and may include remixes of 1980s pop hits. This category of commercial trance music encompasses a range of styles, and boundaries are a bit blurred. Tags on such items tend to include, in various combinations, Progressive Trance, Progressive House, Euro House, Trance, House, and sometimes Techno. Example artists in this commercial/clubby category from the late 1990s and early 2000s include DJ Tiësto, Ferry Corsten, ATB, William Orbit, Dirty Vegas, Tall Paul, Peter Rauhofer.