What is the difference between observation and variable?
In your case, 'n' is the number of observations, and 'm' is the number of variables.  Think of a table in a database - each row is a 'record', and each record has various properties.  A record corresponds to an observation.  Each property is a variable or property of that observation. 

In some contexts people make a distinction between data (i.e. observations, things observed) and variables (parameters to learn - things that vary in a mathematical sense).  But in the context of the link you sent, a variable is a feature.