Semiconductors have majority charge carriers depending on how they were doped. These charge carriers can move around in the material and conduct electricity.
If we connect a p-type semiconductor and an n-type semiconductor to each other, we end up with a region where no charge carriers can move.
Visualize: when connected, the holes of p-type and electrons of n-type near the border area end up combining with each other, cancelling out and creating a region without charge carriers.
So the donors in n-type near the border have lost an electron to recombination; similarly the acceptors in p-type have lost a hole to recombination. Since the donor and acceptor atoms are fixed in the crystal and cannot move, they end up creating an electric field (& potential).
So in n-type, the area near the depletion region is positively charged; similarly in p-type, the area near the depletion region is negatively charged.
So our depletion region has no charge carries, but has a potential difference across it.

That’s the equilibrium state of a p-n junction.

Forward Bias

Connect the p-type to the positive terminal of a circuit and the n-type to the negative terminal. So current is flowing into the p-type and out of the n-type.
So when the current flows through p-type and reaches the depletion region, it carries along the holes from p-type toward the region. Making the depletion region thinner.
Similarly as the current leaves the n-type region, it pushes the electrons back toward the depletion region, making it shorter from this side too.
With enough current/voltage (which?) the depletion region can be made short enough that charge carries can jump across it.
Once a charge carrier jumps across the depletion region, it quickly recombines and burns away.
Electricity keeps flowing though.
Does depletion region ever vanish?

Reverse Bias

Connect the p-type to the negative terminal of a circuit and the n-type to the positive terminal. So current is trying to flow into the n-type and out of the p-type.
This makes the depletion region wider increasing resistance across it so that almost no current flows through.