Ab9#11 is Ab, C, Eb, Gb, Bb and D — with the raised eleventh added on top.
It sounds wide and glassy, bright rather than tense. The ♯11 clears the major third by a whole step, so it adds height without the collision a natural eleventh makes.
Dominant — the lydian dominant sound.
Also written Ab9(#11), Ab9+11 or Ab9♯11.

Ab9#11 is a dominant with its tension raised, so it still points at — harder than a plain seventh does. A plain dominant has two voices a semitone from home; an altered one has four, because every altered tone is also sitting a semitone from a note of Db. More voices leaning the same way is all "more tension" means here.
Every note of Ab9#11 is in Ab lydian dominant.
Each of those is a page: the scale across the neck, and the chords it harmonises into — which is where Ab9#11 sits in it. Every scale.
Change one note of Ab9#11 and you have (drop the sharp eleventh), (drop the fifth) or (the sharp eleventh becomes the thirteenth).
Ab9#11 is an altered chord — a dominant seventh with its fifth or ninth moved. Altered dominant chords on every root.
The common shapes and the derived voicings come from different places, and both are explained in how this site is built.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.