So you've got a couple questions, eh? I'll try to explain.

1. What's a Fandom?
A fandom is like a kingdom, in a sort of way. A kingdom is made up of a group of people who are governed by a king (hence: KINGdom). A fandom is a group of people (fans) who are governed by a certain book, movie, show, person, or popular interest. We call this interest "canon." Fans write fanfiction, make icons, discuss fan-related stuff, and generally obsess.

2. Why "My Fandom"?
When fans make "My Fandom" icons, they generally substitute the words "My Fandom" for a character's name. It is also used to represent the whole fandom on occasion. Kinda hard to explain, because they're so simple, but take a look at some of my icons, and you'll get the picture. Thanks!

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