Low quality flag sends a question into the low quality posts review queue. For questions which enter this review queue, 2k+ users can choose from the option Looks OK, Edit, Close (or Recommend Close). For answers the last option is Delete (or Recommend Deletion) instead.
If you choose should be closed flag, the question enters the close votes review queue. In this review queue, 3k+ users can choose between the options Edit, Leave Open, Close. (As already mentioned in the comment, for users with privilege to cast close votes, there is no actual difference between this type of flag and casting a close vote. A flag is automatically converted to a close vote. However, a close vote pushes the question into the review queue, too.)
For details on when a review of a post is finished, see here: When is a review task "completed" or "invalidated"? A question is removed both from the close votes review queue and from the low quality posts review queue immediately after it is closed (or deleted).
Some network-wide guidelines on what posts should be flagged as VLQ can be found here: When to use the flag “low quality”? The official description of the low quality flag is: "This question/answer has severe formatting or content problems. This question/answer is unlikely to be salvageable through editing, and might need to be removed."
I will add that for posts which are bad enough to consider a low quality flag, users with sufficient reputation might also consider voting to delete. (The reputation needed is 10k for questions and 20k for answers.) Posts which meet some criteria are automatically deleted by a system after a certain time, but sometimes it makes sense to vote to delete manually. In fact, there already have been some related discussions on this meta: Proposal to more aggressively delete off-topic questions or Should we try to re-start manual deletions or is the situation fine anyway? Still, I think that it might be useful to leave some time so that the feedback why the post was closed actually reaches the OP.