The Book of Common Prayer lays out 3 roles for Presbyters in the church: Pastor, Priest, and Teacher. It may seem strange that Priest is included in this list since "priest" comes from a contraction of the word "presbyter". It is almost like saying one of the roles of being a priest is to be a priest.
However, the word "priest" is often used to refer to a very specific task. When we see the word in translations of the Tanakh (Old Testament), it refers to those who conducted religious sacrifices for worship in Ancient Israel. In the Middle Ages, the term "priest" often referred solely to the role of clergy in leading Communion (also referred to as "Mass", "Eucharist", "Lord's Supper", etc.). Other religions also use the term "priest" in relation to sacrifice or worship.
When we speak of the role of the presbyter as priest, we mean the task of helping to lead worship. As the Examination in the "Ordination of Priest" puts it:
You are to preach, to declare God's forgiveness to penitent sinners, to pronounce God's blessing, to share in the administration of Holy Baptism and in the celebration of the mysteries of Christ's Body and Blood, and to perform the other ministrations entrusted to you.
These are all the parts of typical corporate worship that presbyters preside over. Presbyters, though, never do the work of worship alone because that service requires all of us as believers together. Presbyters merely help facilitate worship for all of us together. In this way, the presbyter recalls the function of the priests of old and helps act as a mediator in the service representing the people to God and Christ Jesus to the people. In this way, the presbyter as priest acts as a bridge bringing all into a closer relationship with God through our Lord Jesus Christ.
See The Oxford Dictionary of the Christian Church for more information.