When the value is negative and the firm is the paying side, a default of the firm would relieve it of part of its payments. DVA reflects this in the value. Calculated with the same method and inputs, the firm's DVA has the same size as, and the opposite sign to, the CVA that the counterparty calculates on the firm.
Under capital adequacy rules, DVA is deducted from Common Equity Tier 1 (CET1) to prevent moral hazard.