Sometimes some girl says: I'm on the market, what does it mean?
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Without further context, I would assume that the girl is not seeing anyone at the moment (she is not in a relationship), and she is looking for someone to be in a relationship with.
On the other hand, she may indeed be telling you (on the phone for instance) that she is out shopping. (Thank you Edwin Ashworth!)
The relevant idiomatic expression is...
The "base" expression to be in the market [for something] means you're actively seeking to acquire [something]. In general, if the thing sought isn't either explicitly specified or obvious from context, it means a romantic partner or relationship.
Because of the nature of that extremely common "implied" target, I imagine some people think of "I'm in the market" as meaning "I am available" (i.e. - someone else can "acquire" me), since semantically it would amount to much the same thing. But that "inverted" sense never applies if context clearly indicates anything other than a relationship, so I'd say it's just a misreading of the expression. Also note this...
2b is one of the very few contexts where on can be used at all (effectively it means we = our house is on the housing market (i.e. - for sale). Whereas 2a is the more standard We're looking to buy a house.
TL;DR: For the literal sense it's always in the market (or at the market). For idiomatic usages, it's always on the market = for sale, and in the market = seeking to buy (or get in some other way).
EDIT: It seems several people here accept "non-facetious" usage of "I'm on the market" meaning nothing more than "I'm actively seeking a partner", so it's worth noting that as a possibility. But my advice would be only use it of yourself if you're aware of the "I'm available to be chosen" connotations (as opposed to "I'm looking to make a choice" with the standard form). And I'd certainly advise caution with the on form if you're talking about someone else.