Of course you can find a lot of detailed, and probably more technical and precise information on websites such as this one: Fairtrade Foundation UK, but having worked in the field for the last 8 years I will give you my understanding of it.
Fairtrade seeks to help people in developing countries trade their way out of poverty. This means, on the producer side, that people receive a 'fair' minimum price as well as a premium for development. It most cases it also means that they can develop relationships with buyers that often transpires in technical assistance, capacity building and general guidance, all of which helps them improve the quality of their products and to become more competitive and resilient in the international markets in which they trade in.
On the consumer side, people can recognise and choose products which carry (in the UK) the below label:
The label tells consumers that the company that bought and commercialised the product has adhered to internationally agreed Fairtrade standards.
There are other labels and much debate about other types of 'ethical' trade certifications, but for the purpose of this Blog, I will not go into that and will simply limit my 'cooking experiments' to products that carry this one.