It is important to understand that MATLAB stores data in column-major order, so you know what happens when you apply the colon operator without any commas:

>> M = magic(3)
M =
     8     1     6
     3     5     7
     4     9     2
>> M(:)
ans =
     8
     3
     4
     1
     5
     9
     6
     7
     2

I tend to think "MATLAB goes down, then across". This makes it easy to reshape and permute arrays without scrambling your data. It's also necessary in order to grasp linear indexing (e.g. M(4)).

For example, a common way to obtain a column vector inline from some expression that generates an array is:

reshape(<array expression>,[],1)

As with (:) this stacks all the columns on top of each other into single column vector, for all data in any higher dimensions. But this nifty syntactic trick lets you avoid an extra line of code.

MATLAB stores matrices in column-major order. This is one trait MATLAB inherited from FORTRAN, together with 1-based indexing with round parentheses, and a name spelled in all caps.

When you use linear indexing, as in A(:), you are effectively accessing elements in the order in which they are stored. As another example, reshape(1:12,3,4) produces the matrix [1 4 7 10; 2 5 8 11; 3 6 9 12], because reshape does not move the data, only changes how they are divided in columns.

Functions like sum or any also run down the columns of a two-dimensional array to produce a one-dimensional row vector in one linear traversal.

Storage of a vector is unaffected by the choice of order, and transposing a vector is a constant time operation in MATLAB. All that is needed is swapping the number of rows with the number of columns.

There are some aspects of MATLAB where one may perceive a bit of inconsistency. For instance, subplot(2,2,2) (divide the plotting window in two rows and two columns and select the second of the four parts) selects the subplot in row 1, column 2, but by and large, knowing that the memory layout is column-major helps one predict the results of matrix manipulations and write more efficient code.