Cookies are a kind of short term memory for the web.  They are stored in your browser and enable a site to 'remember' little bits of information between pages or visits.

They are widely used to make the web experience more personal, which is generally seen as a positive thing. However some cookies collect data across many websites, creating 'behavioural profiles' of people. These profiles can then be used to decide what content or adverts to show you. This use of cookies for targeting in particular is what the law was designed to highlight. By requiring websites to inform and obtain consent from visitors it aims to give web users more control over their online privacy.