The .* operator performs element-wise multiplication.
The ' character has at least three potential meanings that I can think of offhand.
The first potential meaning is that of the complex conjugate transpose.
A = [1 2+3i; 4 5+5i]
B = A'
Note that each row in B contains the same values as the corresponding column of A, except that complex numbers are replaced with their complex conjugates.
The second potential meaning is to create a char vector. This could be what Sara Boznik meant with "you use it usually when you want to have something displayed in Command Window."
The third is relevant inside a char vector. Two ' characters will create a single ' stored inside the char vector.