Above is a good introduction to matlab written by my professor. To see how useful matlab is, you need to find a class that benefits from it greatly. For me, I'm using matlab in my signals and systems class, and I am stunned how many built in functions and features the language has. For example, I can plot the impulse response to an LTI in 3 lines of code, I can make a graph of some random function in 3 lines of code, and I can interface functions with each other in the easiest, most streamlined interface I've ever used in programming. In C++, you'd need to mess around with tons of syntax that says "this function I've written belongs to this piece of code. Therefore, that piece of code can use it." In matlab, I put a function.m file in the same folder as my program.m, and I can immediately use the function.m in program.m. It's fantastic! The tons of built in functions cover many areas of math and engineering. It can do differentiation, integration, statistics, signals and systems, and probably tons of other topics I don't even know about. Another powerful feature about the language is that most variables are automatically arrays. The language seems designed to handle enormous arrays and enormous amounts of data.
Commandline is great to test features out before you put it in your script file(the parallel of a program). It's also good to debug/expand an already made script file, because after the script file runs, all of your data is still in matlab's memory. With that, you can, using commandline, input commands to manipulate, test, or view that data.
The best source to see matlab's use would be taking a class that can benefit from the power behind matlab, or maybe reading a book about matlab for engineers.