In the Catholic Christian tradition, statues and icons are venerated, not worshipped. Iconolatry and idolatry (the worship of icons, statues, and effigies as idols) play no part in the healthy spiritual and devotional life of mature Christians. Rather, statues offer a visual aid for worshipping Jesus as Lord, and venerating (honoring) Mary and the saints as those who point the way to Jesus.
On the 12th centenary anniversary of the Ecumenical Council of Nicaea II, Pope John Paul II wrote:

The believer of today, like the one yesterday, must be helped in his prayer and spiritual life by seeing works that attempt to express the mystery and never hide it. That is why today, as in the past, faith is the necessary inspiration of Church art. . . Authentic Christian art is that which, through sensible perception, gives the intuition that the Lord is present in his Church, that the events of salvation history give meaning and orientation to our life, that the glory that is promised us already transforms our existence. Sacred art must tend to offer us a visual synthesis of all dimensions of our faith. Church art must aim at speaking the language of the Incarnation and, with the elements of matter, express the One who "deigned to dwell in matter and bring about our salvation through matter" . . . Duodecimum Saeculum (Veneration of Holy Images), December 4, 1987