Hey Chris!
When used like this, you can think of 並 as a negative version of 眞的 - "really not".
最近老師們佈置的作業並沒有很多,所以我過得相當輕鬆。
Recently (my) teachers haven't set much homework, so I've had it pretty easy.
我上個禮拜去了一趟湖南,然而我並不是很喜歡。
I went to Hunan last week, but I really didn't like it that much.
現在下的雨並沒有很大,而且操場上的雨水也並沒有很多
It's really not raining that heavily at the moment, and there really isn't much lying water on the running track either.
我覺得這個課程對你的漢語進步並不會提供大的幫助。
I think this course won't really help you improve your Chinese that much.
Laurence