I officially started using Photoshop at around the age of 12 years old. It was in the early 2000's and quickly became my favourite hobby. Well back then, many of the "Graphic Designers" in my age group had a website or a MSN Group. Banners were known as "Blends"... you know, the first large image you see on a website or layout. It was very popular and most of the Blends consisted of models or celebrities. It was meant to be fun, playful, and unique. Every blogger or designer had their own style and it was fun because you could join and trade links to a variety of websites.
Buttons were used to trade links with other websites. They are tiny small rectangular images that are meant to represent your website/identity. If your button is on another bloggers website, then it technically means that you have become quick online friends.