Push To Store status you can see on some of the products in My Products means they are not yet live on your online store.
If you want to see only the products with this status, then click on the tab Push To Store found on top of the Products page.
Once you click on the button Push To Store your product will appear live on your online store.
You need to click that button in order to have those products online in your store and be able to sell them.
Keep in mind to make sure you only push to store the products you are absolutely sure you want to sell.
Also, read carefully all the information on every product so you are aware of the specification and the specific requirements of suppliers.