Java has always not just been a language, but it brought us libraries and frameworks. Some of them proved to be bad ideas, some become hyped without having any obvious advantages, but some were really good.
In the JEE-stack, messaging (JMS) was included pretty much from the beginning. In those days, when Java belonged to Sun Microsystems and Sun did not belong to Oracle, an aim was to support databases, which was in those days mostly Oracle, via JDBC and so called Message oriented middleware, which was available in the IBM-world via JMS. JMS is a common interface for messaging, that is like sending micro-email-message not between human, but between software components. It can be used within one JVM, but even between geographically distant servers, provided a safe network connection exists. Since we all know EMail this is in principle not too hard to understand, but the question is, what it really means and if it brings us something that we do not already have otherwise.
We do have web services as an established way to communicate between different servers across the network and of course they can also be used locally, if desired. Web services are neither the first nor the only way to communicate between servers nor are they the most efficient way. But I would say that they are the way how we do it in typical distributed applications that are not tied to any legacy. In principal web services are network capable and synchronous. This is well understood and works fine for many applications. But it also forces us to block processes or threads while waiting for responses, thus occupying valuable resources. And we tend to loose responsiveness, because of the waiting for the response. It needs to be observed that DB-access is typically only available synchronously. In a way understandable because of the transactions, but it also blocks resources to a huge extent, because we know that the performance of many applications is DB driven.
Now message based software architectures think mostly asynchronously. Sending a message is a „fire and forget“. There is such a thing as making message transactional, but this has to be understood correctly. There is one transaction for sending the message. It is guaranteed that the message is sent. Delivery guarantees can only be given to a limited extent, because we do not know anything about the other side and if it is at all working. This is not checked as part of the transaction. We can imagine though that the messaging system has its own transactional database and stores the message there within the transaction. It then retries delivering it forever, until it succeeds. Then it is deleted from this store as part of the receiving transaction. Both these transactions can be part of a distributed transaction and thus be combined with other transactions, usually against databases, for a combined transaction. This is what we usually have in mind when talking about this. I have to mention that the distributed transaction, usually based on the so called two phase commit, is not quite as water proof as we might hope, but it can be broken by construction of a worst case scenario regarding the timing of failures of network and systems. But it is for practical purposes reasonable good to use.
While it is extremely interesting to investigate purely message based architectures, especially in conjunction with functional paradigm, this may not be the only choice. Often it is a good option to use a combination of messaging with synchronous services.
We should observe that messaging is a more abstract concept. It can be implemented by some middle ware and even be accessible by a standardized kind of interface like JMS. But it can also be more abstract as a queuing system or as something like Akka uses for its internal communication. And messaging is not limited to Java or JVM languages. Interoperability does impose some constraints on how to use it, because it bans usage of Object-messages which store serialized Java objects, but there are ways to address this by using JSON or BSON or XML or Protocol Buffers as message contents.
What is interesting about JMS and messaging in general are two major communication modes. We can have queues, which are point to point connections. Or we can have „topics“, which are channels into which messages are sent. They are then received by all current subscribers of the topic. This is interesting to notify different components about an event happening in the system, while possibly details about the event must be queried via synchronous services or requested by further messaging via queues.
Generally JMS in Java has different implementations, usually there are those coming with the application servers and there are also some standalone implementations. They can be operated via the same interface, at least as long as we constrain us to the common set of functionality. So we can exchange the JMS implementation for the whole platform (which is a nightmare in real life), but we cannot mix them, because the wire protocol is usually incompatible. There is now something like a standard network protocol for messaging, which is followed by some, but not all implementations.
As skeptical as I am against Java Enterprise edition, I do find the JMS part of enterprise Java very interesting and worthwhile exploring for projects that have a size and characteristics justifying this.