HAT impresses Jesus? Maybe there are more than a few correct answers to this question. However, in Luke 7 it is evident that Jesus was thrilled with the faith of a Roman centurion and the pure spiritual love of a harlot.
First, it was faith that impressed Christ. Of course, we know that without faith it is impossible to please God. The aforementioned centurion had a particular brand of faith that caused Jesus to be amazed. Jesus called his faith "great" faith. You might be familiar with a different occasion where Jesus called Peter's faith "little" faith because it didn't endure; because it was supplanted by doubt (as he walked on water). The centurion who caught Christ's attention did so with a combination of 2 wonderful traits: he was humble, and he gave absolute credence to Christ's authority and power. "I am not worthy for you to come to my house," he said, "Just say what needs to be said and my servant will be healed." So, Jesus commended him publicly. And since he was a Gentile, Jesus used his testimony as an example (and a rebuke) to the sophisticatedly suspicious Jews.
The second great trait which Christ commended here was the great love of a humble whore. She wept at Christ's feet, washing them with her tears and wiping them with her hair. She kissed his feet and anointed them with expensive ointment. She had commendable faith as well (which Jesus also pointed out), and her repentance is evident. Yet Christ emphasized something else above everything else on this stage. He rewarded her for her love. "She loved much," He said. And by the way, she was forgiven of her sins too (even though they were very many). Jesus was thrilled with the love of this societal outcast. Love covers a multitude of sins.