What is the difference between observation and variable? I have a matrix with size m×n that is built from n number of individuals for person identification. So, n is the number of person and m is the number of feature's value for the person.

It makes me confused about observation and variables. What will I call n and m? Which one represents observation and which one represents variable? My confusion will be cleared to you if you visit the following link: How to do SVD and PCA with big data?
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.