Three overlapping words describe the central experience the New Age is organised around: a decisive shift into a higher state of consciousness. They come from different places and are worth keeping apart.
Ascension is the most specific. It descends from the Ascended Masters of Theosophy and of the 'I AM' Activity of the 1930s, beings held to have completed their human evolution and risen to a higher plane while retaining an interest in humanity, and in later New Age use it broadened into the idea of a collective ascension, a raising of the vibration of the whole planet. That collective sense attached itself strongly to the year 2012 and the end of a cycle in the Maya Long Count, publicised through Jose Arguelles and the Harmonic Convergence of 1987; when 2012 passed without visible transformation, the language survived by becoming open-ended.
Awakening, or spiritual awakening, is looser and older in its roots, drawing on the genuine vocabulary of religious enlightenment but used in the contemporary current for any sense of having seen through ordinary consciousness to something realer behind it. It carries less specific machinery than ascension and is correspondingly harder to date or to pin down.
Kundalini awakening is the one term here with a real and ancient source that modern use has substantially altered. In Hindu tantra, kundalini is an energy imaged as a serpent coiled at the base of the spine, raised through disciplined practice under a teacher up through the chakras to the crown. The traditional setting is one of long preparation and supervision. The modern Western use often describes a spontaneous awakening, self-diagnosed and unsought, and this is where an honest account has to note documented harm: the sudden or forced rising of kundalini is associated in both the traditional literature and in contemporary clinical reports with real and sometimes severe distress, what has been termed 'kundalini syndrome' and treated within the wider category of 'spiritual emergency'. A vocabulary that frames such an episode purely as a stage of enlightenment can discourage a person from seeking help they may need.