It's the same as "Every second Thursday". For example, "Every Thursday" means Thursday every week, "Every other Thursday" means every Thursday every two weeks.

从这个礼拜开始， 下下个礼拜四

For example, this is a series of dates for a meeting "every other Thursday, starting this week." First meeting, Thursday October 15th. No meeting, Thursday, October 22nd. Meeting, Thursday, October 29th. No meeting, Thursday, November 5th. Meeting, Thursday, November 12th. And so on.