What does the size of the multicoloured circle mean?

When you're catching a Pokémon, there is a coloured circle inside the white circle. This circle goes from green to yellow to red. I'm guessing this colour represents the difficulty of capturing that Pokémon because yellow-red Pokémon seem to break free a lot.

However that circle varies in size and goes from being overlaid over the white circle all the way down to tiny little circle I can barely see.

Here the green circle is at max size.

What does this size actually mean? Is it distance that your Pokéball was from the Pokémon or something else?

The ring and its colours are detailed in the official FAQ for Finding and Catching wild Pokémon.

The colour of the ring represents the catching difficulty of the pokémon.

A green ring indicates the capture is low difficulty, orange indicates intermediate difficulty, and red indicates extreme difficulty.

The size of the ring represents your increased chance of catching the pokémon.

You have the greatest chance of capturing the Pokémon while the colored ring is at its smallest diameter. At the opportune moment, fling the Poké Ball toward the Pokémon.

The smaller the ring, the better chance of catching the Pokémon.

Larger ring = nice throw (10xp)

Medium ring = great throw (50xp)

Smallest ring = excellent throw (100xp)

Curve ball = 10xp