You say that something "is on the market" when it's being sold publicly.

Examples of things that can be "on the market" include:

• houses that are being sold
• products that a company is selling
• a company that is ready to be bought by another company can be said to be "on the market"

It's a bit of a joke, but you can also say that a person is "on the market" if they've just become single and are ready to date people:

Watch out, ladies! I'm back on the market.

When you first start to sell an item, you "put it on the market".