The first Bible reference that comes to mind is Jacob's blessing of Isaac (Gen. 27:28). Countless times in the Gospels Christ blesses something, the most notable that comes to mind is the bread and wine at the Last Supper: "And whilst they were at supper, Jesus took bread, and blessed, and broke: and gave to his disciples, and said: Take ye, and eat. This is my body (Matt 26:26)." When Christ cured the sick He blessed them, etc.
At it's most basic elements a blessing is just the minister of the Church invoking a Divine Benediction upon a person or thing. The power to Bless comes from the Holy Spirit which a priest receives in his ordination (as well as the jurisdiction to give the blessings which the priests of the Church can give) but there are blessings that non-priests can give. As a parent, I can (and do!) bless my children in the evening before they go to bed (something the parents can do as the spiritual heads of their household through the power and gifts of the Holy Spirit, as alluded to in the above citation of the patriarchs of the old testament blessing their offspring).