Kabbalah (Notes primarily from Joseph Dan's "Kabbalah: A Very short Introduction".)
Kabbalah is complex, fluid subject with a written history of development spanning about 800 years. There are many forms of contemporary Kabbalah studies. Some of the worship forms used in Neo-Paganism can trace their development through Dion Fortune (aka Violet Firth) and Israel Regardie, The Golden Dawn, 19th Century Free Masonry and Theosophy (H.P. Blavatski) to Renaissance Christian Kabbalah. Kabbalah's practice in the last two centuries (at least) is a mystical one, although its earlier Jewish roots were more scientific.
Briefly (and incompletely), Kabbalah is a cosmology, a metaphysics, and a tool used to contemplate one's relationship with Deity. Kabbalah states that the universe was created by a series of utterances or emanations, called sefirot, from deity. The structure of sefirot is called the Tree of Life. Imbalances in flow of divine power through and to the sefirot strengthen the Left-Hand, or evil powers. Restoring the proper flow aligns the restorer with cosmic or divine powers.
Within (Western European) Neo-Paganism, Kabbalah's influence is most readily seen in theories behind divination by Tarot card -- a particular card is a reflection of a specific sefirot's functioning. Kabbalah's Tree of Life paradigm can be (and has been) used as a template by Neo-Pagans and occultists as a comparative table of world religion by assigning various cultures' gods and goddesses to particular sefirot on the Tree of Life.
Christian Kabbalah's source materials can be traced back to the early 1500's; the most well-known English writer from this time would be Robert Fludd. Its Christian authors were interested in using Kabbalah as a system of magic, numerology and alchemy.
Jewish Kabbalah's written source materials probably go to the ninth century, with claims of an older oral tradition. These are the "Sefer Yezira" (The Book of Creation), probably written in the ninth century; the "Book Bahir," written around 1185; and the "Zohar," written by Rabbi Moses de Leon (d. 1305) and collected in a single printing in 1560.
It is possible to speculate (and the author wishes to point out that this is only speculation on his part) that Dion Fortune's theories of male and female polarity as two ends of a magical battery may trace their roots to "Book Bahir," which introduced gender polarity to Kabbalah by presenting the "Shekhina" as the cosmic bride / divine wisdom.
Earlier writing on Shekhina presented this as an ungendered concept for the limited human perception of Deity. Writings of Lurianic Kabbalah after 1572 also may have influenced Fortune's magical theories, as they suggested bringing the Shekhina into an eroticized union with the deity as expressed through the sixth sefirot (associated with Fortune with the Messiah in general and Christ specifically) would increase and correct the flow between the sefirot.
To the best of this author's knowledge, there is no connection between Shekhina -- a divine (and later a feminine) manifestation of deity -- and Ashera -- an 11th century BCE goddess.
What Kabbalah contributes to Neo-Paganism is: a worldview that words or utterances have a causal relationship with the cosmos; (paradoxically) a worldview that is mystical and beyond verbal expression; erotic union (i.e. The Song of Solomon) as a metaphor for divine knowledge of deity; theurgy, or the idea that humans can help and influence divinity by their actions; and that ancient sages had an esoteric toolkit for influencing the spiritual and divine that allows practitioners to regain a lost relationship with deity.