Free users have limited bandwidth for their accounts, and that limit is set to 10GBs of bandwidth per month .
Bandwidth consumption is counted by the amount of data that is transferred from your account to other sites across the web. The size of the image/video will increase the amount of bandwidth you are using when linking them out to other sites.
Lets say you have 100 photos that 1MBs in size each, and you are linking every single one of them out to your blog/website. 100 images at 1MBs in size means that you are linking out just under 100MBs in data size for all those images. Those photos would need to be viewed 100 times a piece to reach the 10GB Bandwidth cap.
If you only linked out 10 photos that are 1MB in size, those 10 photo would need to be viewed over 10,000 times before you would reach the 10GB bandwidth cap.
If you had 10 videos on your blog/website that were 100MBs in size, that would equal out to just under 1GB in file size. If those videos were viewed 100 times total, you would reach the 10GB bandwidth cap.
If you do reach the bandwidth cap for the free account, your linked out photos will be replaced by a Photobucket image that states "this account has exceeded its bandwidth". The only way to have that image removed over your photos is to upgrade to a Plus subscription, or wait for your bandwidth to reset for the month. Your bandwidth will reset to zero every month on the day you registered your account. You can find this date in your User Settings, under the Account tab.
If you upgrade to a Plus account, you will no longer have to worry about the bandwidth exceeded message, as all Plus accounts have unlimited bandwidth.
Upgrading to a Plus account will only remove that message from photos that are linked out from your upgraded account. It will not remove the bandwidth exceeded message from images that are linked out from another users account.
Having users return to the site to view your photos through direct links does not use any bandwidth. Bandwidth is only used when the image is posted on another site to be viewed.