The butt of something is one end of something, usually the blunt, wider end. A butt is also the remainder of something, like a cigarette butt. Butt can also be a slang word for your buttocks.
Chaff is the husks and stalks that are leftover when freshly harvested grain is threshed. Chaff can be used as a fuel or animal bedding.
The core of something is the inside or center of something. The picture is of an apple core, which is inside an apple in the middle. Sometimes people use the word 'core' to mean the most important part of something, like a core election promise.
Dregs is the residue left behind after something else has been taken away. Dregs usually refers to the poorest quality part of something that has been left behind, or the worst of something, as in "the dregs of society".
Driftwood is wood, usually branches from trees, that has fallen into the water and then drifted around for a while before washing up on a beach that may be a long way from where it fell into the water. Driftwood is often polished smooth by the waves and water, and bleached to a dull grey.
Dust is very fine dirt and lint that drifts through the air and settles on surfaces in your house, making them dull and grey. Dust needs to be cleaned up regularly with a soft cloth. The picture is of some cables from the inside of a computer. They are very dusty. When there is a storm that picks up a lot of dirt in the air, it is called a dust storm.
Filth is disgusting, dirty waste. You might also use filth as an insult, for example "you people are all filth".
Garbage is things that you don't need that have been thrown away. Another word for garbage is trash or rubbish.