Is it illegal to explain someone else's research paper on my website?
As long as you don't quote too extensively from the paper, but do formally quote as needed, you should be fine.
Giving credit avoids plagiarism. Avoiding excessive quoting avoids possible copyright infringement.
But cite the &quot;paper&quot; itself, not just the &quot;paper author&quot;.
I've assumed that you have proper access to the paper.