Most offers are only available in the store but some do say you can use it for an online purchase. In that case, here are the steps to follow:
1) On the app, click on Push to Redeem
2) Select a location - the one nearest to you would be great!
3) You will see a screen with a Promo Code - use that code on the website where it asks for your promo code to get your discount.
See the example below for reference.
Example PushSave Coupon:
Screen shot from Bed Bath & Beyond website: