It’s a conductor. There are free charges (free to move throughout the bulk of conductor). So, in presence of external field, these charges experience a force.
And here's the most crucial bit:
“These charges rearrange themselves until they no longer experience a force.”
As electric field is switched on, electrons move against electric field and accumulate at one side of metal. Naturally, other side gets positively charged. So, the result is an internal field due to the accumulation of charges. The charges in middle stop moving a bit later because the internal field has exact same strength as external field.
(The red dots represent positive charge accumulated on another side. Note that they are not protons)
Inside the conductor, now there are actually 2 equally balanced opposite Electric Fields. So net field inside the conductor is zero.