Complex sentence: The Higgs field has a "Mexican hat-shaped" potential with nonzero strength everywhere (including otherwise empty space), which in its vacuum state breaks the weak isospin symmetry of the electroweak interaction.
Split into simpler sentences: The Higgs field has a "Mexican hat-shaped" potential. Consequently, the field in its ground state has a nonzero value everywhere (including otherwise empty space), and breaks the weak isospin symmetry of the electroweak interaction.