Implied volatility is not one number. It differs by strike and by time to expiry, and the whole set of them is the volatility surface: a function of two variables that fully describes how the market is pricing optionality on a given underlying.
Two cross-sections have names. Fixing the expiry and varying the strike gives the smile or the skew: how implied volatility changes as you move away from the money in each direction. Fixing the strike and varying the expiry gives the term structure.
Skew is the more informative of the two for a directional read, and its sign differs by market in a way that reveals what participants are afraid of. Equity index options are skewed toward puts: downside strikes carry higher implied volatility, because the dominant hedging demand is protection against a fall. Crude has historically shown periods of call skew, because a large class of participants is short the commodity through their operations and needs protection against a rise. The skew is a map of where the hedging demand is.
A surface has to satisfy internal consistency conditions, and this is where fitting comes in. Certain shapes admit arbitrage: if the implied prices across strikes are inconsistent, a butterfly or a calendar spread would have a guaranteed profit. Parametric families such as SSVI are used precisely because they are arbitrage-free by construction, so a fitted surface cannot accidentally imply a free lunch the way an interpolated one can.