What is a merchant?
A merchant is a company or web site that sells products or services.

What is an affiliate?
An affiliate (or associate) is a company or web site that promotes the products or the services of a merchant.

What is affiliate marketing?
An affiliate promotes a merchant's web site (and products / services) by creating traffic from their site to the merchant's thereby earning commission.

What is an affiliate programme?
A merchant (or third party) creates an affiliate programme that an affiliate can join agreeing to promote the merchants products / services.

This can be done using banner ads which the merchant will provide to the affiliate when the affiliate joins the programme.