Essentially its a programming/computing environment which you program using the Matlab programming language.
It's aimed mainly at the fields of maths, science and engineering.
There are also a lot of toolkits which make programming certain tasks a lot easier, for example I've used Matlab (at university) mainly for artificial intelligence based work. As there are toolkits that provide easy to use neural networks, genetic algorithms etc...
As for the cost, you can usually get it a lot cheaper if you are a student.
But yeah generally if you don't know what it is, or you haven't been told that you need it for your job/academic work, then it's unlikely that you need it.