DIFFUSION ACROSS A BOUNDARY WHERE THE CONCENTRATION IS
ZERO ON ONE SIDE AND A CONSTANT ON THE OTHER
Initially the concentration for all x > 0 (to the right of the vertical blue line) is A. As time progresses, material diffuses into the space on the left of the line, which lowers the concentration to the right of the line. As in the previous example (and indeed in all diffusion processes) material moves as the square root of time.
The solution of the equation is really just a statement to the effect: "this is the solution", although it does tell you that if t increases by a factor of 4, you need to increase x only 2 fold to find the same concentration. The function erf(), is the integral of the Gaussian curve, and can be looked up in tables, or can be computed using a number of algorithms, usually implemented on a computer.