If you have cloud-print ready printer it is not compulsory to keep your computer on. If you have a classic printer you should connect it to Chrome browser using your Google account in advanced settings section. Here is the guide for getting started with Google Cloud Print: http://www.google.com/landing/cloudprint/.
Some other features:
- Internal file browser (supports: pdf,jpg,jpeg,docx,ods,xls,xlsx,ppt,odp,txt,doc,xps)
- You can share your printers with your friends
- Mail, SMS, Web page printing
- Printer management
- Print job management