It could mean that...

1) He must be married.

2) Polygamy and/or concubines are strictly forbidden.

3) A divorced person should not serve as a bishop.

4) A deacon could not remarry if widowed.

Through the centuries considerable support has been given to the fourth explanation. Those who believe this favor the translation "married only once." Against this view, it is urged that the Greek words do not necessarily imply that a bishop cannot be married more than once, but merely says that he is to be "Husband of one wife," that is, that he may not have two or more wives at one time. It is also pointed out that nowhere in Scripture is remarriage after the death of a first spouse condemned, nor is it considered detrimental to spiritual leadership.

One fact is clear, the bishop is to have an untarnished record of marital fidelity, which would serve as a worthy pattern for his flock.