As a noun:
* The teacher provided a clear explanation of the concept.
* I'm still waiting for an explanation for the delay.
* Her explanation was unconvincing.
* Can you give me a brief explanation of how this works?
* The detective needed more explanation before he could solve the case.
As a verb:
* He explained his absence with a flimsy excuse.
* Could you explain what you mean by that?
* She explained the problem to the manager.
In phrases:
* In explanation of my absence, I was sick.
* For further explanation, please consult the manual.
* Beyond explanation, the beauty of the sunset took our breath away.
The use of "explanation" depends on the context of your sentence and what you are trying to convey.