I know women cannot be priests because Jesus chose only men to be apostles. A priest recently said another reason is because of the nuptial meaning of the body. What does this mean?

To speak of the nuptial meaning of the body, means that the very design of our body orients us toward a marital relationship. The man is meant for the woman, the woman for the man. And in this complementary relationship which we call marriage, there is the fruitfulness of children. In effect, our body says to us, "You were made for another who will complement and complete you, making your love fruitful." 
 
This is also an image for the spiritual life, wherein God speaks of his relationship to his people in marital imagery. Israel was frequently described as God's bride. In the New Testament, Jesus is the Groom and his Church is his bride. The Church and her members are called to relate to the Lord, to be completed by him and complemented by him such that their love bears fruit. 
 
The sacrament of Holy Matrimony is also a sign of God's relationship to his people, he the groom, we the bride. Even celibates manifest the nuptial meaning of the human person. A priest is not a bachelor. He has a bride, the Church. Religious sisters also manifest a marital relationship, where Jesus is the Groom, they are his bride. 
 
To speak, therefore, of the nuptial meaning of the body, is to insist that the sexual distinctions of male and female are not merely arbitrary physical aspects. Rather, they bespeak deeper, spiritual realities that we must learn to appreciate, and respect. Men and women are different, and manifest different aspects of God's relationship. Women manifest the glory of the Church as bride. Men manifest the glory of Christ as groom. 
 
In terms of the priesthood, this is important, because Christ in his humanity, is not simply male, he is groom, and the sacred liturgy is a wedding feast; Christ the groom, intimately with his bride the Church. 
 
Thus, your pastor is invoking rich theological teaching, which helps to explain one reason why Christ chose only men for the priesthood.