It is a type of software application that displays adverts of some kind while it is running. Sometimes developers will offer a 'free' version of their software on the condition you have to view adverts, they get paid by the number of people clicking on the ads. Quite often there is also a paid version of the same software that is advert-free.
A darker meaning of adware is as a form of 'spyware'.
The application gathers information of your browser surfing habits so that adverts you see on other web sites are tuned to your own interests.
For example, you may have bought some electrical tools on a perfectly ordinary online shop, then you may notice that other web sites begin to advertise similar products when you visit them. This is done by tracking cookies on your computer informing the ad server of your interest in electrical tools.
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