According to the application, MyXperia will be a service or an app which will grant the user the ability to upload and download content from... somewhere, presumably the cloud. With more and more companies offering some kind of cloud storage or service, Sony couldn't allow itself to fall behind the others. Here's what the trademark application offers as a description for MyXperia:
How many of you guys are currently using some cloud storage service on their smartphones?
source: OHIM (use trademark No: 011197332) via XperiaBlog