What does the size of the multicoloured circle mean?

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

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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