The left side of the smile is the haven and funding effect: in a crisis, dollar liabilities are covered and liquidity is hoarded, so the dollar strengthens even if the crisis began in the US. The right side is the growth and rate effect: when US growth and yields lead the world, capital arrives for the return.
The dip in the middle is the synchronised global expansion, when capital leaves the dollar for higher returns elsewhere and the commodity bloc and emerging markets do well.
It is a heuristic rather than a model, and it fails often enough to be dangerous as a standalone signal. Its value is in framing why the same dollar rally can have two completely different explanations depending on what else is happening.
Example: the dollar gains 6% on a trade-weighted basis during a global risk shock, gives it back over a year of synchronised recovery, then gains again on a US-led growth surprise. Three moves, two different causes.
Related: safe-haven-currency, reserve-currency, trade-weighted-index, flight-to-quality