The yield curve risk is how your portfolio will react with different exposures based on how the yield curve shifts.
Investors portfolios tend to move in a parallel shift on the yield curve. This happens when all maturities on the yield curve move by an equal amount. The yield curve encompasses all maturities in the fixed income market. In a parallel shift, the investor would see an increase or decrease in all maturities by, for example, 25 basis points.
In the real world, however, the yield curve does not move this way. The curve tends to steepen, or yield an increase in the long end of the curve compared to shorter issues. The curve can also flatten,with yield on the long end decreasing at a faster rate than at the short end of the curve.
Because any measure of interest-rate risk assumes an equal amount of basis point moves on the yield curve, anything will be an approximation of how an investor's portfolio will react. The risk involved here is the degree to which this approximation will not match of the actual yield curve movement.