Wickipedia defines this as follows:
In the Eastern Orthodox Church, economy (economia) is a bishop's discretionary power to dispense with church standards (or "canons", as they are called) that a parish priest would otherwise be required to follow. Often it amounts to retroactive recognition granted to sacraments performed in heterodox churches when a person converts to Orthodoxy, or in Orthodox jurisdictions with which the bishop's jurisdiction is not in full communion.
Such dispensations are made with a view towards putting the spirit before the letter and helping the cause of the salvation of souls. Generally only bishops can decide to make such deviations. They are seen to be justifiable because the canons are not laws but rather suggestions and guidelines which might, at times, become an impediment.
According to the canon law of the Orthodox Church economia is Ã¢â‚¬Å“the suspension of the absolute and strict applications of canon and church regulations in the governing and the life of the Church, without subsequently compromising the dogmatic limitations. The application of economia only takes place through the official church authorities and is only applicable for a particular case. Because of this concept, in the Eastern Orthodox Church, Love, Mercy, and Compassion remain more in control than absolute law.
The normal case should always be akribia, or strict adherence to the standards. Economia means leniently. Akreveia means strictly.
In orthodoxresearchinstitute response on marriage and divorce one may also find an explanation/definition of Economia:
The question arises here, what is this Ã¢â‚¬Å“economiaÃ¢â‚¬Â exactly? In a theological, scholarly contribution, the present Ecumenical Patriarch Bartholomeos, while still the Metropolitan of Philadelphia, explained in a clear and concise way what Ã¢â‚¬Å“economiaÃ¢â‚¬Â is. He suggests that it is generally accepted that the ecclesiastical economia is an image of the divine economia and love and kindness. That the economia is as old as the Church itself is evident from a reading of the New Testament. This is very clear for example in Acts 16, 3 Ã¢â‚¬Å“so he circumcised him because of the Jews who lived in that area, for they all knew that his father was a GreekÃ¢â‚¬Â. However the economia in the Orthodox Church has never been systematically or officially defined. Ã¢â‚¬Å“It concerns a characteristic, a true privilege and precious treasure of the ChurchÃ¢â‚¬Â. In the pan orthodox meetings of the 20th Century there have been attempts to give a definition to economia, but in the end this has been abandoned, Ã¢â‚¬Å“because economia is something that is rather experienced than described and definedÃ¢â‚¬Â¦in the Orthodox Church, in which it is a characteristic and ancient privilege".
But now the question remains, what is Ã¢â‚¬Å“economiaÃ¢â‚¬Â? Well, according to the canon law of the Orthodox Church economia is Ã¢â‚¬Å“the suspension of the absolute and strict applications of canon and church regulations in the governing and the life of the Church, without subsequently compromising the dogmatic limitations. The application of economia only takes place through the official church authorities and is only applicable for a particular case.Ã¢â‚¬Â This is allowed for exceptional and severe reasons, but creates no precedent. The Church, which continues to extend ChristÃ¢â‚¬â„¢s redeeming work in the world, has on the basis of the LordÃ¢â‚¬â„¢s commandments, and of the apostles, determined a number of canons. Through these the Church helps the believers to come to salvation. But it should be noticed that these rules are not applied on a juridical basis, for the Church always holds in mind what the Lord Himself has said: Ã¢â‚¬Å“The Sabbath is made for man, and not man for the SabbathÃ¢â‚¬Â (Mark 2, 27).
A canon is a Ã¢â‚¬Å“ruleÃ¢â‚¬Â or Ã¢â‚¬Å“guideÃ¢â‚¬Â for the service of worship, the sacraments, and the governing of the Church. There are canons determined by the apostles, the Church Fathers, the local, regional and the general or ecumenical councils. Only the bishop, as head of the local Church, enforces them. He can enforce them rigidly (Ã¢â‚¬Å“akriviaÃ¢â‚¬Â), or flexibly (Ã¢â‚¬Å“economiaÃ¢â‚¬Â), but Ã¢â‚¬Å“precisionÃ¢â‚¬Â is the norm. Once the particular circumstance has past - that demanded a conceding and accommodating judgement Ã¢â‚¬â€œ Ã¢â‚¬Å“akriviaÃ¢â‚¬Â assumes once again her full force. It cannot be that the Ã¢â‚¬Å“economiaÃ¢â‚¬Â, which was necessary in a specific situation, should become an example and should be later be retained as the rule. The Ã¢â‚¬Å“economiaÃ¢â‚¬Â is for the Orthodox Church a notion that cannot be compared to Ã¢â‚¬Å“dispensationÃ¢â‚¬Â in the Roman Catholic Church. Dispensation is an anticipated exception, which provides a juridical norm parallel to the official regulation.
Economia is based on ChristÃ¢â‚¬â„¢s command to his apostles: Ã¢â‚¬Å“Receive the Holy Spirit. If you forgive anyone his sins, they are forgivenÃ¢â‚¬Â (John 20, 22-23). This is the case when the human marriage experience becomes impossible, due to the spiritual death of love. It is then that the Church Ã¢â‚¬â€œ as the Body of Christ Ã¢â‚¬â€œ with understanding and compassion and out of personal concern, can apply the Ã¢â‚¬Å“economiaÃ¢â‚¬Â Ã¢â‚¬Å“by accepting the divorce and not rejecting the sinful humanly weak believers, or depriving them from GodÃ¢â‚¬â„¢s mercy and further grace.Ã¢â‚¬Â It is the precise goal of economia that the weak person not be irrevocably banned from the church communion, according to ChristÃ¢â‚¬â„¢s example, who came, after all, to save the lost.
Orthodoxwiki provided the following brief explaiantion:
Oikonomia (also spelled economia or economy) literally means "household management," the "law of the house," or "house building," and refers primarily to two related concepts in the Orthodox ChurchÃ¢â‚¬â€the divine plan for man's salvation and the specific episcopal application of the canons in the life of the Church. The latter usage is a derivation of the former.
It later expands this a bit more in the issue of Charismation of Catechumens:
Although normally administered in conjunction with Baptism, in some cases chrismation alone may be used to receive converts to Orthodoxy through the exercise of economia. Although practice in this regard varies, in general (especially in North America) if a convert comes to Orthodoxy from another Christian confession and has previously undergone a rite of baptism by immersion in the Trinitarian Formula ("in the Name of the Father, and of the Son, and of the Holy Spirit"), he or she may be received into the Orthodox Church through the sacrament of chrismation, after which receiving the Holy Eucharist. If, however, a convert comes from a Christian confession that baptizes in the Name of "Jesus only" (such as some Pentecostal churches) or from one that does not practice baptism at all (such as Quakers and the Salvation Army), baptism is a prerequisite for chrismation. The use of economia is at the discretion of, and subject to the guidelines imposed by, the local bishop.
As we can see economia is a charism or role played by Bishops only. A priest acts on the direction of his bishop when economia is utilized and works from the directions given by his bishop.