This from the OCF web site: http://www.ocf.org/OrthodoxPage/prayers/molieben.html
Molieben (from Church Slavonic Mol'ba - prayer, supplication) is a short liturgical service usually centered on a particular need or occasion: the new year, a journey, an illness, an act of thanksgiving, etc. It may be addressed to Christ, the Mother of God, or to saints. Its general structure is that of Matins, and it can be served either by request of the faithful or by decision of the parish Priest.
The Church asks us to "pray without ceasing" - Prayer is the life of the Church and the life of each one of us, members of the Church. And because Christ came to redeem and to sanctify the totality of our life, no part of that life, no human need, no occasion is excluded from the Church's prayer. The Molieben, thus, is the extension of the Church's prayer, of Christ's redeeming grace to all aspects and realities of our life. "...knock and it will be opened to you." --we are called constantly to knock at the doors of God's mercy and our faith assures us that God hears us and is with us.
A molieben (also called a moleben, service of intercession, or service of supplication) is a supplication prayer service in honor of either our Lord Jesus Christ, the Mother of God, or a particular saint or martyr. It is a Slavic service, but closely related to the Paraklesis service (of Greek practice--edit mine). A molieben is usually served by an ordained priest, but a laymen can also do a molieben, although in a modified form.
Another informative link:http://www.orthodoxphotos.com/readings/beginning/occasions.shtml
As far as the 40 days of prayer following someone's death, we have this also in the Slavic churches, but this is totally unrelated to the molieben service. This is more a continuation of the funeral service, with each mini-funeral (usually no more than about 10-15 minutes) of the forty days being called a Panikhida (Pah'-ni-HEE'-da).