I don't consider most of the terms developer specific, but I'll give you a quick recap (google could have done the same for you):
UI = User interface, ie. the part of any program that you interact with - usually in the form of one of more windows that you can close, minimize etc. Most of what a program does is not visible or otherwise "detectable" by human senses, and thus it's normal to separate the two.
Java is a programming language, but it is also something more - it's a "concept" where you have something called a virtual machine running on a computer. When a Java Virtual Machine (JVM) is installed and running, that computer can run Java programs. Normally a program runs directly in the Operating System (OS), but with Java it's different. While this complicates things a bit, the advantage is that you can make a program that, in theory at least, can run on any computer running a JVM - making it OS or platform independent. Where it not for this I can't possibly think that UMS would have been available for OS X, none of the developers use OS X as far as I know.
Swing is one of several UI libraries for Java - that is - code that is made available to others that make it easier to create a UI.
Binary/Executable is the name of a program in machine readable form as opposed to source code which is the human readable form. Some languages are
compiled/converted from source code to binary while it's running so that all you ever need is the source code (E.g Python, Perl). A Java executable isn't a "true" executable since it can only be run by a JVM, but it's still common to call it a binary or ar
JAR (Java Archive).
Heap space is more complicated so you'll have to read about it if you want to know what it is, but it has to do with how a computer manages its memory. The reason I mentioned heap space is that the error message given from the JVM to UMS is about that.
To run UMS or any other Java program on OS X or any other OS you need to have a working JVM. This is where it seems that the problem is in your case. I have no detailed knowledge of installing and configuring Java/JVM on OS X, so I can't help with that. I can just state that very quickly after starting up UMS runs out of heap space (memory) and crashes. That either means that you either have to little
RAM (Random-Access Memory) on your computer, that the RAM you have are already used by other programs so to little is available for UMS or that your JVM is configured to use to little of the RAM you have. The commands I gave you were just from a quick google for increasing JVM heap space.
As the JVM and UMS are two separate things and the JVM is what seems to be the problem here, it's not much we can do about it. If anyone that has more knowledge about Java on OS X has something to add that would be helpful, but my knowledge of this is close to non-existing as I don't own any Apple product.