The alb is a full body-length white robe worn by the priest and deacon. It originated as a slight modification of first-century dress. This is the bottom piece of the liturgical vestments.
The cincture is a rope or other belt-like instrument that is worn around the waist. It makes the alb a little less flowing and it can serve as a place to keep the stole in place, by placing the stole through the cincture.
The stole is a long, narrow piece of cloth that is worn around the shoulders and drapes down the front of the body. It is the color of the vestments for the day. This liturgical vestment probably originated with a scarf from the first century which became narrower and more ornamented. The stole is worn above the alb and below the chasuble.
This is the large, outer garment worn by priests at mass. It often is flowing, but it can be stiffer and have more room for the priest's arms. It is the liturgical color of the day. It originated as a Roman cloak, which was a single piece of cloth with a hole for the head, and which covered the person entirely. This cloak was adapted to be the outer garment of the priest at mass.
The dalmatic is a deacon's liturgical vestment. It looks similar to a chasuble, but it has sleeves. A chasuble is free-flowing, and the priest puts his arms out from underneath it wherever there is room, but a dalmatic actually has sleeves to put the arms through. It also is colored for the liturgy of the day. This vestment probably originated in a Roman tunic with sleeves.
The cope is worn at special times and liturgies. It is a free-flowing garment in the back and is draped over the shoulders and clasped together in the front. It is particularly worn during Benediction of the Blessed Sacrament and processions.
The humeral veil is a long, narrow piece of cloth draped around the shoulders. It is really only worn at Benediction of the Blessed Sacrament and when carrying the Eucharist in procession. It is utilized so that the priest's hands do not touch the vessel holding the Eucharist as a sign of respect and reverence for the body and blood of Christ.
The cassock is the robe worn as everyday dress by priests. It used to be widely worn, but it has now largely been replaced by a black shirt and pants. It generally had a sash around the waist.