Simple? Compared to this, yes…
In the standard model, the Higgs field is an SU(2) doublet, a complex spinor with four real components (or equivalently with two complex components). Its (weak hypercharge) U(1) charge is 1. That means that it transforms as a spinor under SU(2). Under U(1) rotations, it is multiplied by a phase, which thus mixes the real and imaginary parts of the complex spinor into each other—so this is not the same as two complex spinors mixing under U(1) (which would have eight real components between them), but instead is the spinor representation of the group U(2).
The Higgs field, through the interactions specified (summarized, represented, or even simulated) by its potential, induces spontaneous breaking of three out of the four generators (“directions”) of the gauge group SU(2)×U(1): three out of its four components would ordinarily amount to Goldstone bosons, if they were not coupled to gauge fields. However, after symmetry breaking, these three of the four degrees of freedom in the Higgs field mix with the W and Z bosons, and are only observable as spin components of these bosons, which are now massive; while the one remaining degree of freedom becomes the Higgs boson—a new scalar particle.