  The very-high-energy (VHE, $\gtrsim 100$ GeV) $\gamma$-ray MAGIC observations
of the blazar S4 0954+65, were triggered by an exceptionally high flux state of
emission in the optical. This blazar has a disputed redshift of z=0.368 or
z$\geqslant$0.45 and an uncertain classification among blazar subclasses. The
exceptional source state described here makes for an excellent opportunity to
understand physical processes in the jet of S4 0954+65 and thus contribute to
its classification. We investigate the multiwavelength (MWL) light curve and
spectral energy distribution (SED) of the S4 0954+65 blazar during an enhanced
state in February 2015 and put it in context with possible emission scenarios.
We collect photometric data in radio, optical, X-ray, and $\gamma$ ray. We
study both the optical polarization and the inner parsec-scale jet behavior
with 43 GHz data. Observations with the MAGIC telescopes led to the first
detection of S4 0954+65 at VHE. Simultaneous data with Fermi-LAT at high energy
$\gamma$ ray\ (HE, 100 MeV < E < 100 GeV) also show a period of increased
activity. Imaging at 43 GHz reveals the emergence of a new feature in the radio
jet in coincidence with the VHE flare. Simultaneous monitoring of the optical
polarization angle reveals a rotation of approximately 100$^\circ$. (...) The
broadband spectrum can be modeled with an emission mechanism commonly invoked
for flat spectrum radio quasars, i.e. inverse Compton scattering on an external
soft photon field from the dust torus, also known as external Compton. The
light curve and SED phenomenology is consistent with an interpretation of a
blob propagating through a helical structured magnetic field and eventually
crossing a standing shock in the jet, a scenario typically applied to flat
spectrum radio quasars (FSRQs) and low-frequency peaked BL Lac objects (LBL).
