What color vestments are worn by the Catholic clergy (Roman rite) during Mass, and what is their significance?
One can do no better than quote the General Instruction of the Roman Missal.
As regards the color of sacred vestments, traditional usage should be observed, namely:
a) The color white is used in the Offices and Masses during Easter Time and Christmas Time; on the Solemnity of the Most Holy Trinity; and furthermore on celebrations of the Lord other than of his Passion, celebrations of the Blessed Virgin Mary, of the Holy Angels, and of Saints who were not Martyrs; on the Solemnities of All Saints (November 1) and of the Nativity of St. John the Baptist (June24 ); and on the Feasts of St. John the Evangelist (December 27), of the Chair of St. Peter (February 22), and of the Conversion of St. Paul (January 25).
b) The color red is used on Palm Sunday of the Lord’s Passion and on Friday of Holy Week (Good Friday), on Pentecost Sunday, on celebrations of the Lord’s Passion, on the “birthday” feast days of Apostles and Evangelists, and on celebrations of Martyr Saints.
c) The color green is used in the Offices and Masses of Ordinary Time.
d) The color violet or purple is used in Advent and Lent. It may also be worn in Offices and Masses for the Dead.
e) Besides the color violet, the colors white or black may be used at funeral services and at other Offices and Masses for the Dead in the Dioceses of the United States of America.
f) The color rose may be used, where it is the practice, on Gaudete Sunday (Third Sunday of Advent) and on Laetare Sunday (Fourth Sunday of Lent).
g) On more solemn days, festive, that is, more precious, sacred vestments may be used even if not of the color of the day.
h) The colors gold or silver may be worn on more solemn occasions in the Dioceses of the United States of America.
As regards significance,
White is the colour of holiness, of the Church, of the Sacraments [except Penance], and the saints [except martyrs]. It's the colour of rejoicing and is used throughout the Christmas and Easter seasons.
Red is the colour of blood, so it's used for celebrations of Our Lord's Passion and of martyrs; it's also the colour of fire and used on Pentecost and the feasts of the apostles who were touched by the fire of the Holy Spirit on that occasion.
Green is the colour of nature, and is used when no other colour is prescribed.
Purple is used for penitence. Advent and Lent are penitential seasons. It's used for funerals because the requiem mass is one of penitence for the sins of the departed; and it's used for the sacrament of confession [that's obviously penitential!].
Rose is a sort-of watered-down purple. It's used on the Sundays indicated above, which are named after the first words of the introits on the respective days, both normally translated as "Rejoice!" — the penitential nature of these Sundays is relaxed a little.
Cloth-of-gold may be used at any major feast, including for example, the patron saint of the church: the patronal festival is a feast of the first order.
There may be local customs like wearing blue for celebrations of Mary, Mother of the Lord. There are a few anomalies like St John the Apostle & Evangelist, who was an apostle but not a martyr and whose feast falls in Christmastide: he gets white. St John the Baptist has two feasts, and it's white for his birth and red for his death.