Traditional Latin Rite Vestments
Contemporary Latin Rite Vestments
(Above picture taken from Ad manipulum: the maniple as seen in Rome...)
The same blog quoted from St. Thomas Aquinas in the supplement to the Summa Theologica:
Seventh Article
Whether the Vestments of the Ministers Are Fittingly Instituted in the Church?
"I answer that, The vestments of the ministers denote the qualifications required of them for handling Divine things. And since certain things are required of all, and some are required of the higher, that are not so exacted of the lower ministers, therefore certain vestments are common to all the ministers, while some pertain to the higher ministers only. Accordingly it is becoming to all the ministers to wear the amice which covers the shoulders, thereby signifying courage in the exercise of the Divine offices to which they are deputed; and the alb, which signifies a pure life, and the girdle [cincture], which signifies restraint of the flesh. But the subdeacon wears in addition the maniple on the left arm; this signifies the wiping away of the least stains, since a maniple is a kind of handkerchief for wiping the face; for they are the first to be admitted to the handling of sacred things. They also have the narrow tunic, signifying the doctrine of Christ; wherefore in the Old Law little bells hung therefrom, and subdeacons are the first admitted to announce the doctrine of the New Law. The deacon has in addition the stole over the left shoulder, as a sign that he is deputed to a ministry in the sacraments themselves, and the dalmatic (which is a full vestment, so called because it first came into use in Dalmatia), to signify that he is the first to be appointed to dispense the sacraments: for he dispenses the blood, and in dispensing one should be generous."
"But in the case of the priest the stole hangs from both shoulders, to show that he has received full power to dispense the sacraments, and not as the minister of another man, for which reason the stole reaches right down. He also wears the chasuble, which signifies charity, because he it is who consecrates the sacrament of charity, namely the Eucharist...."