Italki has a monthly language challenge every so often. When you join the challenge, you set yourself a personal goal for the month and try to meet that goal. It's a motivational challenge. A '30-day writing challenge' is similar: you promise yourself to write something every day for 30 days. (I don't know if the challenge here is set by a teacher or by the person him/herself). A similar but much more ambitious event is NaNoMo -- National Novel Month. People who participate in NaNoMo try and write a complete novel during the month of November!

I don't know for sure, but it sounds like a challenge to write something and post it in your Notebook every day for 30 consecutive days.