According to Rabbi Aaron Wertheim, Rabbi Pinchas of Koretz (1726–1791) stated, "The acronym for Shabbos is: Shtreimel Bimkom Tefillin -- the shtreimel takes the place of tefillin." Since wearing special clothing on Shabbat is a form of sanctification, among the Hasidim of Galicia and Hungary, the shtreimel is associated with the holiness of Shabbat, a crown such as that worn by royalty, which enhances and beatifies Shabbat.
There are those[who?] who say that to wear a shtreimel is to wear a crown. Viewed from atop the head, the ring of tails is wrapped clockwise spirally connoting that the spiritual forces invoked by the shtreimel are radiating in such a fashion as to invoke the Divine Presence to become more tangible in creation. even asserts that the number of furs used in the manufacture of the shtreimel has some significance. Common numbers are 13, 18, and 26, corresponding respectively to the Thirteen Attributes of Mercy, the numerical value (gematria) of the word for life (Hebrew: חי), and the numerical value of the Tetragrammaton. Contemporary shtreimlach may include higher numbers of tails. At least one maker creates shtreimelach with 42 tails, symbolizing the 42-letter Divine Name.
3. Arnon, Dan (1995). A Hat for all Season. Tel Aviv: Am Oved. ISBN 965-13-1021-9, p.88
4. Halachos V'halichos B'chasidus, p. 196
As to the [who?], I have heard that from various chassidim too. Furthermore, the Crown is a reference to Keser, the top-most sfira from which all Divine influence emanates, which is then linked all the way down to the this-worldly Kingdom – Malchus – representing Shabbos. In other words, by wearing a crown (shtreimel), we bring down the Divine light into our otherwise mundane Shabbos-observance.