Matlab is one name that refers to many things (quite like Java). It is a programming language as well as an interpreter as well as a set of libraries. The language is vector-based, making it very easy to write mathematical or data-manipulating applications very easily and quickly. There are also very useful toolboxes for things like visualizing data, designing digital filters, machine learning, statistical analysis, etc. However, it is an interpreted language making it slower than a language like C or Java.
Matlab is commercial software that can be bought from www.mathworks.com. However, students can obtain fully functional versions that have one restriction: matrices cannot be larger than 100 X 100.