Take, for example, this passage from Acts 3:
1 Now Peter and John were going up to the temple at the hour of prayer, the ninth hour. 2 And a man lame from birth was being carried, whom they laid daily at that gate of the temple which is called Beautiful to ask alms of those who entered the temple. 3 Seeing Peter and John about to go into the temple, he asked for alms. 4 And Peter directed his gaze at him, with John, and said, "Look at us." 5 And he fixed his attention upon them, expecting to receive something from them. 6 But Peter said, "I have no silver and gold, but I give you what I have; in the name of Jesus Christ of Nazareth, walk." 7 And he took him by the right hand and raised him up; and immediately his feet and ankles were made strong. 8 And leaping up he stood and walked and entered the temple with them, walking and leaping and praising God. 9 And all the people saw him walking and praising God, 10 and recognized him as the one who sat for alms at the Beautiful Gate of the temple; and they were filled with wonder and amazement at what had happened to him.
One of my problems when I do Lectio Divina is that I frequently just can't get beyond the surface. Other times, I will start out very dry, but after about 20 minutes, some phrase will suddenly break open and reveal something I hadn't seen before.
In this passage, you have a lame man sitting outside the Beautiful Gate asking for alms. He's lame, and he's sitting outside the Beautiful Gate seeking money. Peter and John come along, and Peter gives him, not what he's looking for, but "strength" to walk. Peter gives the man what he has from Christ, and that "something" allows the lame man to stand up and enter the temple through the Beautiful Gate.
So we might be seeking what we think we need: wealth, security, love, fame. But until someone passes on what they have been given from Christ, we're unable to walk through that Beautiful Gate. We're seeking alms outside the temple rather than entering the temple, walking and leaping God's presence.