Well, I am sure, you can find a lot of definitions on this on google but, if you have to understand it via an real time example, here it is.
Most of us do online shopping and order stuff. Lets take Amazon as an example for our online shopping partner. If you are looking for a product in Amazon today for products which bikers need for a long trip and leave the mobile app or web without adding any items to cart or purchasing anything, the next time when you login to the app or web, amazon will show the products as recommended based on your previous search. These are in other terms called as customer preferences.
How does Amazon know that these were refereed by your earlier? It has programs, bots, algorithms which does the keyword based analysis and comes up with the recommended recommendations based on customer and their preferences. The tasks which programs, bots, algorithms do is nothing but the automated data mining.
If you are in India and if you consider the recent demonetization and what central government is planning to do with the cash deposits done post the announcement sacking the rupees 500 and 1000 is also data mining. They would have collected all the deposits which have happened in all the banks (both private and govt based) and running the algorithms or doing the analysis to fetch all the deposits which are done beyond 5 lakhs of rupees and getting the PAN card of the customer and fetching the contact details like the email and phone and sending out alerts to show the reason for deposits.
Not only for this, once they receive the data from the customers even that data can be mined to see the most commonly used reasons and based on those the govt can formulate more tough laws to crub the corruption and black money.
Data mining is mostly used by organizations (for business development, customer satisfaction), governments (as described above) and people who need to analyze large volumes of data and make sense of it for some purpose or the other.
Another simple example can be IT guys surfing for opening based on their technology, even that can be considered as data mining.