24:23 He ordered the centurion that Paul should be kept in custody,
and should have some privileges, 
and not to forbid any of his friends to serve him or to visit him. 
24:24 But after some days, Felix came with Drusilla, his wife, who was a Jewess,
and sent for Paul, and heard him concerning the faith in Christ Jesus. 
24:25 As he reasoned about righteousness, self-control, and the judgment to come, 
Felix was terrified, and answered, "Go your way for this time, 
and when it is convenient for me, I will summon you." 
24:26 Meanwhile, he also hoped that money would be given to him by Paul, that he might release him. Therefore also he sent for him more often, and talked with him. 

24:27 But when two years were fulfilled, Felix was succeeded by Porcius Festus,
and desiring to gain favor with the Jews, Felix left Paul in bonds. 
 

The most interesting and applicable verse in this section is verse 25. If you were Paul what would you preach to Felix? With antinominan easy-believism pervading modern evangelicalism I would suspect most would simply try to get Felix to pray a prayer in an experimental fashion to receive Christ. But we see both in the examples of Jesus and Paul that much of their preaching involves helping people to develop saving faith and not simply to make a decision or to pray a prayer of salvation. We saw in the case of the rich man in Luke 18 who asked Jesus directly what he had to do to be saved, but Jesus saw that he needed further preparation before he could receive the good news. So also with Felix. As with many apathetic fence-sitters, Felix lacked conviction of sin. He lacked the fear of God. But in speaking to him of issues of righteous behavior and self-control and God's judgement Paul helped to develop these in preparation for him to receive the gospel. (Self-control is seldomly preached today, for it deals with behavior. And behavior is a subject antinomial types don't like to deal with. What does that tell you about modern evangelicalism?) 

As with most of the people of Israel wandering in the desert so Felix appears to not to desire the promise land but rather to go back to Egypt.  For it is one thing to have conviction of sin and fear of God's judgment, but it is another to react to such in faith. Those who react against the gospel usually have one of three responses. There are those like the Jews then are openly hostile against it. Then there are those who become false Christians and try to change the gospel inside the Christian community. But there are also many like Felix here who simply run away.

vs 26 Also reveals Felix's attitude. I don't think he was completely insincere in his discussions with Paul, but certainly there was an element of greed. His allowing Paul a degree of freedom to be ministered by other Christians would allow for them to provide Paul with money for bribery in Felix's mind which Felix probably looked upon not as sin but rather simply as the way things are done in his own culture, much as is also a common practice in mainland China today. Such people again reveal the corruption of their spirit through their lack of conviction of sin in such matters.