British Airways is the flag carrier and the largest airline in the United Kingdom based on fleet size, and a founding member of the Oneworld alliance. British Airways merged with Iberia in 2011, creating the International Airlines Group (IAG) and it is the world's third largest airline group in terms of annual revenue and second-largest in Europe.
Executive Club is the frequent flyer programme of British Airways and has 4 different tiers: Blue, Bronze, SIlver and Gold. Due to the merger with Iberia, changes were made to the Executive Club to maximise integrations between the airlines and IAG operated loyalty programme, Avios. You may refer to this link for more information on Avios.
To join British Airways' Executive Club, you can simply register online here.