Q. 1. What does it mean that a priest is suspended?
A. 1. It means that a priest has been removed in part or in full from his ministerial activies as a cleric and that some his faculties may be restricted. In simply words, he may no longer be able to act as a parish priest, nor to celebrate Holy Mass or wear a Roman collar in public. Each situation is different, depending on the reason for the suspension, such being outlined by the Bishop in his letter to the priest.
The Code of Canon Law related to this matter is:
Can. 1333 §1. "Suspension, which can affect only clerics, prohibits:
1/ either all or some acts of the power of orders;
2/ either all or some acts of the power of governance;
3/ the exercise of either all or some of the rights or functions attached to an office.
§2. A law or precept can establish that a suspended person cannot place acts of governance validly after a condemnatory or declaratory sentence.
§3. A prohibition never affects:
1/ the offices or the power of governance which are not under the power of the superior who establishes the penalty;
2/ the right of residence which the offender may have by reason of office;
3/ the right to administer goods which may pertain to the office of the person suspended if the penalty is latae sententiae.
§4. A suspension prohibiting a person from receiving benefits, a stipend, pensions, or any other such thing entails the obligation of making restitution for whatever has been received illegitimately, even if in good faith."
Some reasons for suspension are changing the liturgy (words of the Mass), distributing communion contrary to Catholic teachings (non-Catholics, gay community, etc...), drug dealing, physical or sexual abuse of a child or adult, refusing an appointment by his Bishop, sexual activites (relationship with a woman), supporting abortion, supporting homosexuality, supporting married priests, supporting same sex marriage, theft of Church funds, etc... This list serves as an example only; it is far from complete.
Suspensions can be temporarily or permanent, depending on the situation.
Suspensions can be appealed to the Vatican’s Congregation for Clergy. When a priest appeals his suspension, the execution of the penalty is suspended until such time as the Vatican has made a decision on the matter.
Can. 1353 "An appeal or recourse from judicial sentences or from decrees, which impose or declare a penalty, has a suspensive effect."