to bless: to speak a good word over someone or something, whether praising God, calling down God's favor on a person, or actually granting that favor
This verb is built from two pieces that mean "good" and "to speak," so at root it is to speak well of someone. From that one idea the New Testament fans out in several directions, and the direction usually depends on who is speaking and who is being spoken about.
When people aim the word upward at God, it means to praise him: God gains nothing, but he is honored with good words. When the word moves downward, from God to people or from someone in authority to those under them, it carries real weight: a blessing pronounced by God actually brings the good it names, and a blessing pronounced by a patriarch or priest was understood to set a future in motion. In between sits the everyday command to bless other people, even enemies, which means to speak good over them and ask God's favor for them rather than curse them.
Two settings became fixed customs. One is the blessing said over food at a meal, close to what many still call saying grace. The other is the welcome cry "Blessed is he who comes in the name of the Lord," a set phrase of honor that the crowds shouted to Jesus.
What holds all of this together is the good word itself. Praise, favor granted, and good wished on an enemy are all the same act pointed in different directions, which is why one verb covers the whole range.