Dependent Exemptions refer to the number of children that you claim on your taxes. In addition to dependent exemptions, other noteworthy exemptions include a new spouse or other eligible person (parent/grandparent, nephew etc.) that you routinely claim as a dependent on your tax returns. Obviously the more exemptions that you qualify for on your taxes, the lower your tax liability will be.
How this lowered tax liability impacts your ability or need to pay child support depends on whether you are the Obligor (higher earner/payor of support) or the Obligee (lower earner/recipient of support). For the Obligor, the greater number of exemptions you have, the greater your ability is to pay child support as more of your income is being kept by you as opposed to being paid to the IRS and the Franchise Tax Board.
For the Obligee, the greater number of exemptions that you have, the less of a need you have for child support as you are able to keep more of your income as opposed to being paid to these same agencies. Although the dependent exemption is typically awarded to the custodial parent (parent with larger custodial time), it may be awarded to the non-custodial parent if the parties both agree. If that is done, the custodial parent will need to complete IRS form 8332 to release the dependent exemption and to ensure that the IRS is clear as to who will be claiming the child on their taxes.