He is trying to verify certain bits of information that you gave him during the date with what you wrote or included on your online dating profile.
In essence, he may be curious about something that you told him during the date and has now gone back to check out your online dating profile after the date in order to get more information about it.
Perhaps there is something that you told him during the date that contradicts or supports what you put on your online dating profile.
However, it is best to do that when the time is right as opposed to when you first meet them.
Being that this is the first time that they are meeting you, away from the safe confines of an online dating site, they may not be comfortable with showing you this kind of personal information.
The people who tend to have the most success with the first date are the ones who don’t get carried away with expectations.
People can often get carried away with expectations for that first date based on how well their interaction has been going with the person that they are interested in online.