My interpretation(And from experience):
The way to look at this is, specific to currencies, at any given point in time a currency’s forward curve exhibits a relationship between it’s interest rates(usually around IRP) based on market participant’s exectations, however the market’s expectation of that can change daily, which is called shifting of the curve in the trade.
This woud expose you of basis for currencies. So when you trade currencies at any point, you actually lock in the spot rate and the expected interest rate differencial at that specific point in time. As time passes before expiration, the interest rate relationship changes and that is your basis risk.