The best replacement for explanation is argument.

The best alternatives to explanation are rated as following:
★★★★★  argument
★★★★  excuse
★★  description
★★  explication
★★  justification
★★  explanations
★★  prediction
★★  explaination
★  explanation
★  definition
★  interpretation
★  instruction
★  another point of view
★  understanding
★  proximate
  exclamation
  exposition
  scientific explanation

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Speaking about explanation, one probably shouldn't forget about pictures.

Other search terms related to explanation and their ratings are:
★★★★★ pictures
★★★★ an example
★★ hadith
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Google Trends

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explanation
argument
excuse