"Cover the fees" allows your donor to pay the transaction fees, thereby allowing the church to receive the whole donation.
When a donor chooses to cover the fees, their total gift is increased so the church receives their desired amount. This means that for the church the effective transaction rate of such a donation becomes 0% and the church receives the whole donation. Generally, more people choose to "cover the fees" than not, so your overall effective transaction rate would be closer to between 0-2%, much lower than PayPal's 2.2% for non-profits.
Additionally, if the donor uses a bank account, then the transaction fee is only 1%. Donors can cover these fees as well, if they desire.
The "Cover the fees" option is not selected by default and the donor will have to choose to cover the fees by clicking a checkbox while making the donation.
For a detailed description of how fees are calculated, please see the following article on Tithe.ly's website: