Analytics broadly describes the process of monitoring usage of your site and pages by individual users. Among other items you can see which country or even city your visitors originate from, how they got to find your site and what they searched for. You can also monitor which pages the visitor interacts with and how long they stay. If you have a shopping options or subscribe/sign-up pages – you could also track when sales are completed or abandoned. Very useful is also to see what kind of device is used to access your pages to ensure best possible design for a variety of devices (i.e. responsive design).
All this information is useful to ensure that your webpages are optimized towards the kind of interaction you are looking for and brings you the desired effect for your business or cause.
Google analytics is the most well known service collecting this information for you. However, you and your visitors are providing Google with very valuable information and are doing so FREE of CHARGE and with the data of you visitors and potential clients. If you value the privacy of your visitors and still want meaningful statistics you need a better solution!
ONE of the better alternatives is a FREE and open software for analytics by MATOMO (previously named PIWIK, hence the title of this page). This software has many features an options and can far outsmart Google while, importantly, keeping the data under your own control. Even if you do not wish to run you own MATOMO, using mine will still not expose your visitors to any data mining as I strictly run my MATOMO instance for my own customers and never use the collection for myself or 3rd parties.
MATOMO is also available in the SaaS option through their website at a monthly subscritption fee. (NO, I am not receiving any compensation for mentioning them here!)
For me, MATOMO analytics is the free and open source alternative of choice for meaningful analytics. There are a few paid options which some people might want to use, but the core of the MATOMO software is free and open source (up to now) and that ensures transparency!
Update: I have implemented two factor authorization on my MATOMO server. A feature I normally install on my WordPress sites too for added security against hacking.