I am reading Introduction to Quantum Mechanics by David Griffiths and I am in Ch2 page 59. He starts out writing the time dependent Schrödinger equation and the solution for $\psi(x,t)$ for the free particle,
$$\psi(x,t) = A e^{ik(x-(\hbar k/2m)t)} + B e^{-ik(x + (\hbar k/2m)t)}$$
Then he goes and says the following,
Now, any function of $x$ and $t$ that depends on these variables in the special combination $x \pm vt$ (for some constant $v$) represents a wave of fixed profile, traveling in the $\pm x$-direction, at speed $v$.
What does this sentence mean?