It means he is concerned about his daughter's feelings. Perhaps he's recently divorced, and making sure his daughter feels comfortable with him dating again. It seems odd to ask permission, but it's nice that he takes her feelings into account.
So be aware that you're getting into a situation where the guy is very close to his daughter. Which is good, but if he's asking her if it's okay if he even gets a woman's number, you can bet that she'll factor into every other decision he makes in your relationship. Particularly in the early stages, he's probably going to be taking things slow for the sake of his daughter. Just something to keep in mind.
Interesting...
Ummm... run, Forrest, run! I've dated guys who are a little "tooo" into their daughter's "feelings".... it's completely exhausting and highly inappropriate that he would involve her so early in a "relationship". It's also very creepy when a divorced man becomes overly attached to his daughter after a divorce. It's like displaced affection they don't know what to do with and it borders on perverted. With this track record, he'll have a revolving door of women coming around his daughter and she will have bigger issues than she already has now. Eventually, he will end up taking the daughter's side on everything and God help you if the daughter decides she doesn't like you anymore. LOL Ultimately, guys like this resent you for coming between him and his precious daddy's girl. It has disaster written all over it. Speaking from many years of "single dad" dating experience.
How our country has fallen so far, when a father's love and concern for his daughter is now seen as perverted. Cannot wait to show my wife this comment...