Implied versus realized
Implied volatility (IV) is the volatility you would plug into a pricing model to get today's option price. It is the market's price for future movement. Realized volatility is measured from past price changes over a chosen window. Both are usually quoted as annualized percentages.
The VIX index is Cboe's measure of the 30-day implied volatility of the S&P 500, calculated from a wide range of SPX options. It describes how much movement the market is pricing, not which direction.
Example: with the VIX at 16, a rough rule says the market is pricing a typical daily move of about 1% (16 divided by 16: a year has roughly 252 trading days, and the square root of 252 is close to 16). That is a one-standard-deviation estimate under a bell-curve assumption, not a cap on the day's range.
Term structure and skew
Term structure compares implied volatility across expirations. A spike at one date often reflects a scheduled event, such as an earnings report or a central bank decision. Skew compares implied volatility across strikes within one expiration. In index options, puts below the price usually carry higher implied volatility than calls above it, which reflects demand for downside protection.
IV Rank places today's implied volatility between its low and high over a lookback period, often a year. IV Percentile is the share of days in that period with lower implied volatility than today. A single extreme day stretches IV Rank more than IV Percentile, so the two can disagree.
The volatility risk premium
Option sellers take on the risk of sudden large moves, and they want to be paid for it. Researchers measure that payment as the variance risk premium: the difference between the variance implied by option prices and the variance that later occurs (Carr & Wu, 2009). It has been found to carry information about future stock returns (Bollerslev, Tauchen & Zhou, 2009).
Caveat: comparing today's implied volatility with past realized volatility mixes two windows: one looks forward, the other back. High implied volatility before a known event, or low implied volatility after one, can look rich or cheap on that comparison without being either.