A swap rate is the level at which a swap has zero value, but the value of a receiver swap is convex in the swap rate (the value falls as the rate rises). When the observation date and the payment date are the same, the expected swap rate is therefore higher than today's forward swap rate. When valuing a CMS, this difference is added as an adjustment to get the expected amount received on the payment date.
Consider a hypothetical example in which the adjustment is positive, the forward swap rate is 2.0%, and the adjustment is 0.1 percentage points. The rate used to value the CMS is 2.1%. On a notional amount of 10 billion yen, one payment of CMS interest is valued at 0.21 billion yen. The extra 0.01 billion yen raises the value for the party receiving the swap rate and lowers it for the party paying. Valuing at 0.20 billion yen without the adjustment underestimates the receiver's side and overestimates the payer's side.
The direction and size of the adjustment depend on the relation between the observation date and the payment date, and the model of interest rate movements. If the interval from observation to exchange equals the tenor of the reference swap rate (a 0.5-year swap rate exchanged half a year after observation), the adjustment is zero.