It's true that you can implement multi-agent programming in other languages, but it's very natural and clear in NetLogo.
PS: I did my PhD in the group that produces NetLogo, and continue to be blown away from the language and what you can do with it, even though I don't use it on a daily basis any more.
I quite like its approach - like you say, it's a very natural way to do agent-based modelling. I also think its a good beginners' language for modellers who know their field (e.g. ecology) but haven't yet learnt how to program. Lastly, I like it's GUI integration.
However, I am somewhat put off by its verbose "toy language" syntax; and I really can't afford its performance. (We are currently working on a model in Julia, and even that can take up to several weeks to compute a single run on our HPC...) So I guess my opinion is that its a fantastic language to learn about modelling, but not well suited to constructing large, complex and resource-intensive models.
I've heard great things about Julia, but haven't ever used it. Yet another thing that's on my list...
The basic idea in agent-based modeling is that you have a bunch of different types of objects, which we'll call "agents." Each agent has its own independent state, which typically includes location and one or more other variables. So far, that sounds like regular ol' object-oriented programming.
However, there are some differences. First, you have all agents of one type act at the same time, at the tick of a clock. You can then say, "Hey! All doctors! Move in the direction of the closest sick patient." You can similarly say, "Hey! All patients! If there's a doctor next to you, then you have a 30% chance of being cured." Then you create a population of doctors and patients, randomly infect some proportion of the patients, and run the model.
The code for what I've just described is very short and very readable. And it does away with the need for loops. You basically describe the action that a class of agent will take at any given moment, and then tell the agents to perform one or more actions.
Again, it makes much of the programming simple and easy to understand. And yet, you can write pretty complex models in this way.
For example, I implemented the Autumn model ( http://ccl.northwestern.edu/netlogo/models/Autumn ) for NetLogo (because my eldest child was asking why leaves change color when we lived in Chicago). So I created a model in which each leaf has some randomly set values for each of the chemicals that affect color change. Then I let the user adjust the temperature and rainfall. The leaves changed colors as a result. It didn't take me much time to implement, and turned out to be a great learning tool.
Agent-based modeling isn't great for everything, but it's great for many things -- especially for modeling complex systems.
What does that even mean? That description fits nearly every commonly used programming language and runtime.