A boarding pass is the document that shows you have purchased an airplane seat and as such should be allowed onto the flight. If you just had paper boarding pass and you lost it, then you could be in serious trouble. Fortunately, with electronically issued boarding passes you can replace your boarding pass easily, and even reference or print out copies of past boarding passes from older flights in case you need them.
Ask for an electronic boarding pass to be sent to your email when you purchase your ticket, or when you go through your travel agent. In order to save paper and to make it more convenient for travelers, most airlines offer electronic passes that are emailed to passengers on purchase.
Save the electronic boarding pass in your email. The pass doesn't get deleted or removed after the flight, so leave a copy in your account. Or, alternatively, save it on your computer or phone so that you have it with you and can print out more copies.
Contact the airline that you flew with. Ask if there is a way that a copy of your electronic boarding pass could be sent to you. If you had a physical ticket you can also ask if a copy can be issued to you. In both cases, the records only last so long, so you will need to move quickly to get the copy of the boarding pass you need.