Linked from
The 16 pages that link to Higgs field, each with the reason it gives.
Higgs mechanismRelated: Its nonzero vacuum value is the background that makes the mechanism operate.
Quantum fieldBroader topic: Its nonzero vacuum value shapes particle masses in the Standard Model.
Electroweak symmetry breakingRelated: Its nonzero vacuum value drives the symmetry breaking.
Electroweak theoryRelated: Its vacuum value is the symmetry-breaking ingredient in the theory.
Electroweak epochRelated: Its changing state drove electroweak symmetry breaking.