A term used in foreign exchange rate quotation.
Consider the historical FX quote:
GBP 1 = 1.4598 - 1.4602 USD.
The base currency is GBP.
This is the currency there is a single unit of, to be exchanged for a variable number of USD.
The inversion of this FX quote means expressing the same price, but with the other currency as the base currency (USD here):
USD 1 = (1 / 1.4602) - (1 / 1.4598) GBP
USD 1 = 0.6848 - 0.6850 GBP.
In the inverted FX quote, USD is the currency there is a single unit of (to be exchanged for a variable number of GBP).
In any market, the reversal of a normal - or commonly expected - relationship.
For example the situation of an Inverse yield curve, where longer maturities of funds are trading at LOWER yields than shorter-dated maturities (being the opposite of the normally expected upward-sloping relationship).