I have asked my PhD supervisor to write a letter of recommendation for me for faculty positions. He has asked me to first write three paragraphs about my research in my current postdoc studies. Is this normal? Why would he need to know about my postdoc research?
Yes, it's normal and very good for him to have this information.
Think about it. Which of the following letters (slightly exaggerated) seems stronger?
I was Adamia's PhD supervisor. She wrote her dissertation on XYZ and obtained nice results on P, Q and R. Since then she has been a postdoc at ABC. I have no idea what she's doing there and I really don't care, it's probably not that interesting.
It shows that you used to be doing good work, but doesn't establish a continuing record. Compare with:
I was Adamia's PhD supervisor. She wrote her dissertation on XYZ and obtained nice results on P, Q and R. Since then she has been a postdoc at ABC, where she has been working on J, K and L, and published two papers in top journals.
If he can address your current work in your letter, he can assert with more conviction that you have an ongoing pattern of success that is likely to continue into a new job.