In everyday terms:
Uncontested divorce usually means the divorce can move forward without a fight in court—either because the other spouse doesn’t oppose it or because the spouses have already resolved key issues (property, support, custody) by agreement.
Contested divorce means there is a disagreement that requires court involvement—either about the divorce requirements themselves (like whether the one-year separation is met) or, more commonly, about related issues like property division, support, or custody.
One NC-specific nuance: North Carolina allows an absolute divorce after the statutory requirements are met (most commonly one year of separation), even if other issues are still being disputed in separate claims.