The market value of a position is normally recalculated with end-of-day market data. Market data is also used to measure risk, and the supervisory guidelines list, as a point of focus, how to choose the data fed into a value-at-risk measurement. If departments and systems use different values, market values and risk measures disagree, so a financial institution decides the sources it loads from, how it checks the data and how it keeps records, and manages market data on that basis.
Consider a hypothetical example in which a position changes in market value by 1 million yen when interest rates move 1bp (0.01%), and the 10-year rate is loaded 10bp higher than the actual rate. The market value is off by about 10 million yen. The direction of the error depends on the direction of the position, and it can make market value and profit and loss look larger or smaller than they really are.
Market data is not the risk factor itself (a factor such as an interest rate or exchange rate that changes the value of a position) but the value of that factor. This site calls the values observed in the market that are used to calculate the market value and the risk measures "market data."