There isn't ONE application that does this. It isn't ONE application that does this in the Apple ecosystem either. They just refer to all of the different things working together as the iCloud. As William Fleming has pointed out, everything syncs to Google, as far as mail, contacts, calendar goes. You just point your desktop email and calendar client (Evolution, Thunderbird, etc) to your Google account and they will stay in sync between your phone and your laptop. A Google/Gmail account is necessary for an Android phone, just as a Apple account is necessary for an iPhone.
For bookmarks, you can use Chrome on your phone and PC, and the bookmarks will stay in sync, provided you log into both with your Google account.
For documents/photos you can use the Dropbox service, and you have 2GB of free shared cloud storage. You can pay for more if necessary. When you install the Dropbox app on your phone, you can set it up so that all photos are automatically uploaded to Dropbox, which will automatically sync with your laptop. Any documents placed in your Dropbox folder on your PC will be instantly uploaded to Dropbox, and you can retrieve them on your phone with the Dropbox app.
Welcome to Ubuntu and Linux in general. I wish you luck!