~0x7f is inverting all bits.

So for an 8-bit number, you get 0x80.
For a 16-bit number, you get 0xff80.
For a 32-bit number, you get 0xffffff80.

And &= is a bit-and. It can never turn on bits, but can clear bits.

In this case, it will clear the 7 low bits.

If you knew you had a 8-bit wide port, you could have written:

P1MDIN &= 0x80;

But if the register was 16-bit wide, you had instead to write:

P1MDIN &= 0xFF80;

In short - going that extra route with ~ to invert the bits, you make sure that the & operation will handle whatever number of bits that the register happens to be wide.