This program can no longer be downloaded. Take a look at Google Photos instead.
Google still hasn't released a version of Picasa for Mac. If you upload your photos to Google's Picasa Web Albums though, you'll need to have this uploader set up on your Mac.
The Picasa Web Albums Uploader looks very much like the Flickr Uploadr: you drag and drop photos on the left side of the window, then select an album, enter a caption and press upload. The upload limit is around 1GB, which is the cap set on your Picasa Web Albums account, quite sufficient for most people. The Uploader can also be used to upload pictures from iPhoto straight to your Picasa Web Albums account. It's not obvious how to perform this, and you'll have to click File>Export then select the Picasa tab from the pop up menu to upload your photos.
Once again, if you have a Picasa Web Albums account, then this application is pretty much indispensable. It's basic but will upload your photos quickly.