In a blog post announcing the new module, Google notes that it has seen mod_pagespeed reduce page load times by up to 50%.
Here's some of what mod_pagespeed does:
Makes changes to pages built by a CMS without having to change the CMS itself.
Recompresses images when the HTML context changes.
Extends the cache lifetime for elements like logos and images on your website to a year, while still letting you update those files.
Google will be working with Go Daddy to get mod_pagespeed running on many of its servers. It is also working with Contendo to integrate mod_pagespeed into its CDN.
When it comes to getting mod_pagespeed running on your own web server -- Google has released it for many Linux distributions (CentOS, RHEL, Ubuntu, Debian, Fedora), but you can also download the source and compile it for your platform as necessary.
If you don't control your own server or slice, you'll need to ask your web host to look into adding mod_pagespeed to its setup.
Check out this video to see mod_pagespeed in action.