with (something), (clause)
When you want to tell the context or the reason for a comment, you explain it with the word "with". For example:
With all the rain we've been having, I bet we'll get some great strawberries this year.
In this example, the reason that the strawberries will be great this year is that there's been a lot of rain.
With the time you put into studying, you should do really well on the TOEIC.
In this example, the reason that you think the listener will do well on the test is that he or she has studied a lot.
With all this down time, I don't know what to do with myself!
In this example, the speaker means that she's not sure how to spend all of the down time that she has now.