What exactly is computer science? I have a question that, no matter how much I think about, I do not have the answer to.  The question is what exactly is computer science?  The reason I am asking is that I went into college thinking computer science was going to be about software engineering disciplines and deep study in the realm of application and practicality; these excited me.  However, after taking core requirement classes for computer science, many so devoted to discrete mathematics (set theory, group theory (abelian properties, etc.), probability, etc.), I became disillusioned and frankly, sick of taking these abstract-concept related courses, asking myself daily when I would use these concepts in my daily life as a developer.  

I've searched online for the answer, but none have satisfied me so far.  Several arguments have boiled down to essentially saying something like "If you want to do gaming, you have to be good at trigonometry, which is math"; clearly, this is not what I am looking for.  If someone could guide me into truly understanding why discrete math and structures is essential to the software engineer, and to the world outside the realm of the academia aspect of computer science, that would be awesome.  Thank you!
"...asking myself daily when I would use these concepts in my daily life as a developer." The answer depends on the job. It sounds like you don't like math/theory, so you would not apply for/ get a job that requires a deeper understanding of CS, as many higher-level jobs do.

However, the truth is that the vast majority of software engineering jobs requires very little math or theoretical computer science, or even a good understanding in computer systems (which you didn't mention). If you just want to write code for websites or applications or do front-end, you can do that just fine without knowing most of the topics taught in a CS curriculum. Most of this knowledge is simply uneccessary, although having a degree will certainly help you get a job. However I know people who went into the software engineering profession with degrees in journalism or theater or other completely unrelated fields.

Also, there are some colleges that offer a degree in Software Engineering, which is much more focused on the practical side, including software development cycles and practices.

This is all practical advice. As for what Computer Science is, there is probably no universally accepted answer. It's a broad field, with many different sub-fields. However, most people would probably not consider simple software programming as Computer Science.