Getting a sense of what is going on with your website can be a challenge, how much traffic, who is coming, where are they going, how long are they staying. One of the best tools for this is the free application from Google called Google Analytics. It is free and pretty easy to install on your site. I highly recommend it and I use it all the time to see what is going on with my sites.
Analytics can be overwhelming because it is kind geeky and has a huge number of reports. But I basically just look at a few areas for that quick snapshot.
1. daily traffic (general trends, web, mobile, tablet)
2. landing and content pages (for me the most important reports)
3. referrals (where traffic is coming from, how do they get here)
4. keywords (what are people using to search for your kind of content)
5. I like the traffic flow charts, (how people move through your site)
After this I move through other areas like time on site, mobile, insights, etc. But mostly it is the quick view that I do.
Below is a quick video I found on helping you understanding a little how it works. I highly recommend installing Analytics on your site and start getting the big picture.