Implied volatility, or IV, is the volatility an option's price implies. Feed the market price into the pricing model and work backwards: IV is the number that makes the model agree with the market. It's quoted as an annualised percentage.
From IV to a daily move
Volatility scales with the square root of time, so a rough one-day move is IV divided by the square root of 365, or about 19. At 60% IV, expect moves of about 3.1% a day, one standard deviation either way.
Implied versus realised
Realised volatility is what actually happened. Implied tends to sit above realised on average because sellers demand a premium for taking on risk. When IV is unusually high, options are expensive; a calm period afterwards rewards the sellers, a violent one the buyers.
What moves it
IV rises ahead of known events, expiries of size and after sharp falls, and it tends to fall during grinding rallies. Market-wide volatility indices average the options market into one number, which is a good way to compare one week with another.