you will receive power ... and you will be my witnesses

The apostles will receive power that will enable them to be witnesses for Jesus. Alternate translation: "God will empower you ... to be my witnesses"

to the ends of the earth

Possible meanings are 1) "all over the world" or 2) "to the places on earth that are farthest away" (See: rc://en/ta/man/jit/figs-idiom)