A weekend is Saturday and Sunday especially when regarded as a time for leisure and in most countries no one works during these two days. I'm sure you know that fact. I'm also pretty sure that you know that in a month there are usually four weekends. Then, a couple of weekends a month, strictly speaking, would mean two weekends out of the entire month. So, what the sentence is saying is that Steve Jobs pays them a visit (he goes there and stays there for a while) every two weekends each month. It can be the first and the second weekends of the month or it can be the second and the fourth weekends of the month etc. The order is not important here, but the fact of the matter is that two random weekends out of one month are spent by Steve Jobs there. The following would be an equivalent statement to your original sentence:
Steve Jobs goes there two times a month.
Are things starting to make sense to you now?