I know active users is unique users that in the data range visit our site. but my misunderstanding point is that what is the interpretation when we use 1-day, 7-day, 14-day together? what is the meaning? each point when click by mouse show a one day, I couldn't get the point. is there any better meaning?
To start out: the Google Analytics Active User report documentation. It may be helpful, but it doesn't really answer your question.
For completeness, let's go through the graph itself to start: Each day along the graph is giving the user count for the time ranges ending on that day. So in your screenshot, in March 8-14 there were 27 active users, and in March 3-9 there were 51 (the number in the popup: 7 days ending on March 9).
The graph then shows you the pattern of those running totals. I would mostly use this myself to view, say, the 7-day total by itself on the graph, to see traffic trends with the day-to-day changes smoothed out.
One use I could think of for viewing more than one line together is this: Suppose you were looking at your 28-day active users on the graph, and the total went up. By graphing the 1-day active users at the same time, you could see whether it was due to a big spike in traffic on one day, or a smaller increase that lasted longer.
