Learn English – What does the phrase “He got nothing on me” mean

The phrase is "what makes one tick"

what makes someone tick

Fig. something that motivates someone; something that makes someone behave in a certain way.

In your dating context it implies you should not just know the person superficially but also get to know what that person is interested in, what motivates them, what are their likes and dislikes - and that will help you have a better relationship.

I imagine the origin of the idiom will be from knowing the internal machinery which makes a clock tick.

I would interpret this anachronistic question as hipster-speak for:

So, what are your interests, employment, education, religion, and/or life goals?

Basically this person is trying to determine whether you would make a valuable acquaintance or possibly sexual partner based on mutual interests.