What does Luke 16:13 mean?

This completes Jesus' application of the parable of the dishonest manager (Luke 16:1–8). People need to choose whether they worship money or God. The dishonest manager tried to serve two masters: his employer and himself. In the end, he made choices with his employer's possessions that benefitted himself, not his employer.

In the Bible, verbs of emotion don't just describe a feeling; they describe a lifestyle based on that emotion. "Hate" means to disregard something, to ignore it. Ultimately, we cannot perfectly split attention and effort between two things. One will always be our real priority. The wise person chooses the eternal God; the fool chooses earthly comforts and pleasures as represented by money.

"Devoted" means to be attached to something, to turn one's attention toward that thing. "Despise" is the opposite; to have contempt for, to devalue something.

Jesus makes it clear that His audience—His disciples—need to decide who is their master. The wise person does not love or have devotion for money. If we put God first, money—and all other life concerns—will naturally fall into the place of priority where they belong. In this case, money will be used to serve and bless others.

This verse makes a chiasm: a poetically mirrored structure. The first and fourth lines are synonymous poetry, as are the second and third:

A. "No servant can serve two masters."
B. "for either he will hate the one and love the other"
B'. "or he will be devoted to the one and despise the other."
A'. "You cannot serve God and money."