You are either insane or just like to speak in extremes, asking for "exactly." No one is going to encapsulate all of human experience with them here. Sorry. You will have to accept grossly poor summaries that capture almost none of it. That said:
They are an arithmetic logic unit plus various peripherals plus pin driver logic plus (typically) several types of small memories and sometimes a bus interface unit all placed upon a monolithic chip of silicon, mounted on a chip carrier and then that assembly encapsulated in an epoxy body, then tested, packaged, and sold.
They are used wherever they save cost or power consumption, reduce heat or size, or provide a useful advantage over not using them -- such as some new feature that would have been far too expensive without them. They are often found in toys for many of those reasons. But they are also present in many if not most electronic devices, today.
"Good" is in the eye of the beholder. If you are making iPads, what's "good" for you will be very, very different than if you are making a one-off widget to blink a few LEDs at home for the Christmas tree. I can tell you what I use. But the whys are personal/business that probably wouldn't mean the same things to you. I use Microchip PIC16, PIC18, PIC33, and PIC32; plus Atmel AT90 and ATmega families; plus ADSP-21xx DSPs; plus a specific SiLab 80C51 that supplies a 1MHz, 16-bit ADC on board; to name some of the current and recent past ones.