Whenever a galvanic cell is explained in textbooks/videos, it usually starts by showing that if you put a piece of $\ce{Zn}$ in a $\ce{Cu^{2+}}$ ion solution, the $\ce{Zn}$ will become oxidized and transfer $\ce{2e-}$ to the $\ce{Cu^{2+}}$ ion, so the $\ce{Cu^{2+}}$ becomes a neutral $\ce{Cu}$ metal.
I understand this, but in a galvanic cell, the $\ce{Zn}$ never actually touches the $\ce{Cu^{2+}}$ ions, the $\ce{Zn}$ and $\ce{Cu}$ are only connected with wires. I don't understand how the $\ce{Zn}$ can be oxidized and transfer ions through the current.