Question

what happens when copper wire is dipped into silver nitrate solutions

Answer 1

copper will take the place of silver . According to the displacement reaction a metal can replace another metal which is placed below in the reactivity series .
So the copper can replace silver from its salt solution.

Answer 2

When copper wire is dipped into solution of silver nitrate, copper being a more reactive metal than silver displaces silver from its compound by forming copper nitrate with a shiny greyish white deposit of silver on the copper wire.
2AgNO3 + Cu -- Cu(NO3)2 + 2Ag