Difference between square brackets and curly brackets in Matlab?

A square bracket creates a vector or matrix, whereas curly brackets creates a cell array.

When working with numbers, I'd say that 99% of the time, you will use square brackets. Cell arrays allow you to store different types of data at each location, e.g. a 10x5 matrix at (1,1), a string array at (1,2), ...

x = [1 2 3]; #% matrix with values 1, 2, 3
y = {1, 'a', x}; #% cell array storing a number, a character, and 1x3 matrix

Here is the MATLAB documentation on cell arrays: http://www.mathworks.com/help/matlab/cell-arrays.html

This paper answered my question above in a very elegant manner. The paper explains Matlab arrays to someone who is more familiar with non-array based languages such as C++, C#, Java, and Python:

MATLAB array manipulation tips and tricks - Peter J. Acklam