I am self taught in Unix as well (as is painfully obvious in some of my assumptions past (and future)). However, I know for a fact in my experience that trying to learn every possible solution to every problem is not possible. You have to understand the system first, then create or figure out your own solutions. Yes, people get stumped sometimes. It's OK to ask for help. But no one will hold your hand for everything.

And if I do honestly think a question is obvious homework (and usually other believe the same) I do not hesitate to close the thread right away. This question may not be homework, but it's such a pointed and narrow question for such a broad subject that many people may take it to be homework.

Anyways, here's a website on old core memory, before the nifty little DIMMs / SIMMs used more recently:
http://www.psych.usyd.edu.au/pdp-11/core.html
Most systems now use moderm memory, but you'll still hear terms that are a throwback to this memory, like "core dump" or "in-core image".
A core file, or core dump, is basically an abnormally aborting process dumping all of it's physical memory to disk. It's useful for debugging. They are typically files called "core". If you use the command "file core", many systems will tell you what process created the file.

Getting rid of unnecessary core files is like taking out the trash at home - if it was never done, your kitchen would eventually fill up.
It may not slow your system down very much, like rotting fruit on your kitchen counter doesn't affect how long you have to bake your cookies, but then again, who wants rotting fruit on their counter?

There lots of maintenance you can be doing - cleaning up core files is one of them. There's also hardware maintenance, software upgrades, etc...

As for finding core files, run as root:
"find / -type f -name core > /tmp/core-list 2>/dev/null"
Next, examine each file to make sure it's not needed by a developer or system engineer, and delete the ones that are just taking up space.

And as for not liking the man pages, after a while, you'll probably start hearing a lot of people telling you to RTFM (Read The F***ing Manual). Man pages are a wonderful resource, and no Unix admin or guru can do without them. Learn how to effectively search the man pages (man -k keyword), and search google for answers, since many people have probably had similar questions in the past. Some systems also use the "info" program, which is like a newfangled man page system. It's a little more interactive, and almost navigatable like html, but frankly, I'll take a man page any day.