To become vastly superhuman or superbaseline and incomprehensible to untranscended beings. To breach a singularity barrier. Transcension is qualitatively different from ascension; an ascended being retains some, or many, of eir previous characteristics, while a transcended being does not (at least as perceived by untranscended entities).
Although a transcended being may remember eir former existence in great detail, that existance generally appears to have little relevance to such a being except as a collection of dispassionate data.
 To become a god or godlike, to attain Enlightenment, to become a power, or a transcendent being, to disappear from manifest existence, to enter into the Cosmic Mind or the Absolute, or realize one always was the Absolute all along.
 (noun) one who transcends, or the act of transcendence, from a lower to a higher toposophic. In doing so, the old faculties drop away - e.g. a Buddha who enters nirvana is a transcend because e no longer retains an embodied existence. Contrast with ascend.
Transcend-Ascend - Text by M. Alan Kazlev One who transcends to one toposophic, then ascends to the next. For example an intelligence may transcend to SI:1, leaving behind everything of itself that was of SI:<1. Then e may ascend to S2, retaining eir SI:1 nature but adding an S2 superstructure on top of the SI:1 nature. Contrast transcend-ascend. Often however the dividing lines are not this well defined
Transcendent Being - Text by M. Alan Kazlev An entity that is distinct from physical existence, whether considered ontologically, as a supernatural or supraphysical being, or soteriologically, as a being that is no longer a part of embodied existence or samsara. The existence of a transcendent being or beings (e.g. God, Buddhas, etc) is central to many religious memeticities, but denied by physicalist memeticities.
Transcension Chasers - Text by M. Alan Kazlev Sentients, very often SI:<1, but sometimes higher toposophics, who spend their lives chasing Ascension and Transcension Events. They go around wearing these holographic T-shirts which play a little movie of the latest big transcendence they recorded, you know, an "I was There when the Croupe-Ngame B MicroCluster made the Big Exponential" They hold conventions, swap collectibles, show off their artifacts, that sort of thing...
Transcension Prediction - Text by Anders Sandberg and M. Alan Kazlev Given the huge population of the civilized galaxy, and the fact that ascensions and transcensions are moderately common and have been going on for thousands of years, many polities and civilizations have developed some fairly reliable methods for predicting the onset of one of these events. Often this is comparable to pre- and post-singularity efforts at predicting the weather (and a large transcendence event does indeed share some conceptual characteristics with a force of nature to those watching from outside at a lower S level).