Picasa is photo editing software developed by Google to manage digital photos & videos. Picasa allows you to organize and edit your photos and videos. DropBox is a cloud storage & synchronization service by DropBox Inc. DropBox allows you to backup photos, videos & files to access them from anywhere. Dropbox allow you to create a dedicated folder (Dropbox folder) on your computer for storing their files, photos & videos. DropBox offers 2GB free storage space. Before you go ahead and move the folder, you can first see how much space you will need on Dropbox.
You can install PicBackMan's Picasa uploader for Mac from the website and start backing up photos and videos.