By saying Eclipse and not specifying any particular language, I'm going to give you my answer from the point of view of Java, which is the programming language that you surely use (although the answer will be the same for all languages):
A program is just a code sequence (a recipe), so when started correctly send all lines of code to the processor in a language that he understands to run one after another until you reach the end . Once reached the end he follows his own and forgets you forever. The possibility that when you re-run the program in the future, remembering something that has happened necessarily means that you read the data somewhere.
Is there a side that is not a database, in your case MySQL, so that these data can be stored there, and that once the program starts read and update them so you can always access them ? The answer is clear: YES. Of course there are ways to save data that does not pass through MySQL, proof of this is that there are different types of database servers as it can be also, SQLite, etc ... that save data in very different ways.
The answer you are looking for from all of them is simpler, and I think I speak from experience since you reminded me when I began my career in Computer Engineering (But where do I keep this so I do not forget it?), in files that you yourself believe in a directory that you have controlled beforehand (probably inside the program folder or in folders like / var or / tmp in UNIX environments)
Saving everything in folders and files so that you know how the data has been saved so you know how to read it will get that home database we are looking for. Entering this topic and answering your question with as much information as possible about it, object serialization deals with exactly this: convert an object into a sequence of bytes to be able to write / read about them without problems.