I use Matlab a lot for my job, and I've come to understand that Matlab is two distinct yet inter-related things: 
  1. It's a programming language
  2. It's an integrated development environment
I was taught a bunch of different things about it in college, ranging from "it can solve equations" to "it can plot things".  But at a more fundamental level, it's simply a programming language.  Or more accurately (I think?), it's an uncompiled scripting language and a script interpreter.  And the Matlab window itself is a development environment which debugs the code, runs it, and stores outputs in memory. 

There are countless other tools that check one or all of these boxes.  But I think two things that set Matlab apart are
  • it's good at array-based math (MATrix LABoratory), e.g; [1, 2, 3] + [4, 5, 6] is simple to do and built in
  • it's a very simple language where a bunch of things work in ways that they probably shouldn't, which makes it attractive for engineers who didn't study computer programming