What are "custom ROMs" in relevance to Android? I have heard custom ROMs before, but I do not know what that's supposed to mean in contrast to Android itself, the physical hardware, or the stored-software it's comprised of.

I know that a ROM is essentially firmware, but in some contexts it can be also understood as a ROM image.

So what does "custom ROM" mean within Android? A customized bootloader or source?

Also, what would be the point of customizing it if it was a firmware image?
A custom ROM is basically any ROM (the Android image) that didn't come from the manufacturer of the device.

As for why you'd do this, there are a few reasons


Some manufacturers don't bother providing updates after device release.  Custom ROMs can provide a newer Android version than the manufacturer and thus provide additional features and security updates.
Also, there are various features that some manufacturers don't include, such as 2-way call recording.  Custom ROMs using custom kernels can provide these features.