Skype needs an excellent internet connection in order to easily transmit the high volume of data that video uses. Your internet connection can be the fastest in the world, but if your partner's is slow, both of your connections will be.
To fix it, you both can do this:
-Make sure all other applications that are using the internet actively are exited. Things that are downloading like large files from the internet can take available bandwidth away from Skype.
-Make sure your computer is close to the router if it is wireless. The closer you are, the stronger your connection.
-Use a wireless connection that doesn't have many users, or use wired connections instead.
Besides this, you could purchase faster service from your ISP, but that is more of an extreme route. Hope this helps!