It's a bebop term.
When you're improvising bebop, the chords are flying by - it's common for tempos to be 240-300bpm, and it's common to have chord changes every couple of beats. That means having to cope with a new chord every half second or so.
Because of the speed, improvising bebop is tougher, and different from, improvising in other genres. So the pedagogy (the "how do you teach/learn" part) of bebop is pretty much a four-step process:
1. Learn to hit a chord tone (ANY chord tone!) at the change. This gets you thinking about what notes are in the chords as they're flying by.
2. Run up (or down) the arpeggio as it flies by. You might only have time to squeeze out four notes... make the note of the next chord as close as you can to the one you're playing in the first chord (e.g. if the change is C9-Fmaj11, you might play C-E-G-Bb / C-E-G-Bb - that's the 1-3-5-b7 of C9 followed by the 5-7-9-11 of Fmaj11). This is a little harder than just picking one tone, and it gets you used to knowing the spellings on the fly; ideally, you want to know chord spellings like you know your multiplication tables, without having to think about them.
3. Alternate arpeggio runs with runs of appropriate scales for the chords. Now you're adding non-chord tones for color.
4. After you've got a feel for that, use tones that lead into the chords. That's what's called an "approach pattern". You're starting just before a given chord, and you're trying to end it on a note that will lead into what you want to do next, whether that's an arpeggio, scale, or a single target tone. That means basic approach patterns really begin with approach NOTES, typically a half step above or below your target. If you're making an approach to Cmaj7, you might play B or Db just before the chord change (or D#/F if you're targeting E in the chord, etc).
More complicated patterns are just extensions of that approach note. Keeping C as a target for a Cmaj7 chord, you could go both above and below Db-C-B-C or B-C-Db-C. You can do three chromatic notes: D-Db-C or Bb-B-C. You can use diatonic notes instead of chromatic ones: D-C-B-C or B-C-D-C. You can skip over the target and return from the other side, either chromatically (B-Db-C) or diatonically (D-B-C).
So you're right that approach patterns create a tension that leads into a main lick. When you're doing bebop, the 'easy' approaches - that is, the ones you have to get down first to be successful - either have no real tension (an arpeggio) or minimal tension (a scale that mates with the chord). Approach patterns break that up, doing something different that precedes a target tone. A good improvisor will mix them to create a structure of tension and release in the big scheme of the solo.
I'm sure there are teachers using the term in other genres, because improvising is really just composition on the fly. I teach all sorts of composition techniques as part of improvisation lessons, and I steal/borrow them (hopefully with due credit to the source) all the time from classical and jazz composers. Most ideas can be easily adapted to fit rock, blues, etc.
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