Explain it like I'm five:
We gather the uranium or whatever from the Earth in small amounts.
We process those small amounts into larger, more useable chunks.
We use those chunks until they are less useful, but still radioactive.
We then dispose of those chunks.
If the material is still dangerously radioactive, why can't we:
Keep using the chunks in another system, or
Reprocess the material so it is still useful, or
Grind it up into the original size and put it back where we found it.