The fullstop (.) operator is for element-wise operation. For example:
A = [1 2 3 4];
B = [5 6 7 8];
AS you can see that A and B both are 1X4 matrices and normal matrix multiplication can not be done. However, lets say you want an output C as [1*5 2*6 3*7 4*8] (i.e. multiply each element with the corresponding element), then you can do
C = A.*B;
The colon operator (:) is a way to write 1:end. In the example here, to access all the element of A, you can write:
A(1,1:4)
A(1,1:end)
or A(1,:)
All 3 a legit way to do this and will give same result.
