The Trinity is how I would describe God: the Father, Son, and Holy Spirit, three in one consubstantial and coeternal essence. To get even more complicated, the Orthodox Church believes that the Holy Spirit proceeds from the Father unlike our Catholic brothers who believe that the Spirit proceeds from the Father and the Son. This is known as the Filioque clause which was added to the Nicene-Constantinopolitan creed in 1014, filioque literally means “and the son,” in Latin which did not previously exist in the creed developed in 325 at the first council of Nicaea.
Does the Trinity fit within the typical definitions of monotheism? I would say that there is certainly a fine line between the Trinity and monotheism but a line nonetheless. Since monotheism calls for a singular God, many could interpret the Trinity as being three different modes of a singular God, like a three dimensional object which only truly occupies only one of the three or a combination at any given time. This is known as modalism, simply put it is the disintegration of the hypostatic (the three divine persons) union of the Trinity, the Trinity has become delaminated. If there was no trinity and it was a singular God, it is at this point which we start to dabble in Monarchianism, the belief that there is a singular God and no division into the three hypostases. The Trinity is not monotheistic or three separate Gods by any means, the Orthodox worship the Father, Son, and Holy Spirit as a singular God.