What Am I Doing Wrong?

I have recently started up a blog site for the first time, and am slowly coming to grips with how everything works. However, every so often something happens that completely baffles me, and I have just hit one of those momments!

What is happening is:
Every time I publish a post, each with a picture and then some writing underneath, it will look really good at first. But then when I return to my site, say the next morning for example, the photos will be gone. When I go into the post to try and edit it to see what is happening, the image frame is still there but the image is just not showing up. The first time I tried to put the image in again, and that worked fine, but a little while later the pics were gone again. So I am just not sure what I am doing wrong? I am putting the pictures in by going to the “insert image” option then typing the URL on the website (not mine) where they are located. Should I be doing it differently?

Any help or advice would be greatly appreciated, however please be as specific as you can, because even if it seems obvious to you…well I am still a giant newbie:)