What is the idiom for the line Whose stern impassioned stress A thoroughfare for freedom beat in America the Beautiful mean?

Answer 1

There are no idioms in that line. It means that the stress of the battle beat freedom's road -- in other words, America was formed as a land of freedom by fighting the British.

Answer 2

The context for that line is this verse:

O beautiful for pilgrim feet,

Whose stern, impassioned stress,

A thoroughfare for freedom beat,

Across the wilderness.

The poet, Kathrine Lee Bates, was from Massachusetts, and she wrote the poem at Pikes Peak, in Colorado, a mile above sea level in the Rocky Mountains. The poem is in the form of a list of reasons that America is beautiful. She addresses the the country: "O beautiful FOR pilgrim feet, whose stern, impassioned stress..." meaning, the "stress" of the feet of those "pilgrims" (impassioned people on a pilgrimage to find freedom, or live free) beat a thoroughfare (made a highway) across the wilderness for others, also seeking freedom, to follow them. In other words, the continuous tread (stress) of all of those pilgrim feet beating flat the grass and wearing smooth the ground, made not just a path, but a thoroughfare, a road, across the wilderness for the generations of freedom-loving people to follow them.