The phrase "improved processor" means that the brain or central processing unit of a device, such as a computer or phone, has been enhanced to work faster and more efficiently in processing information and running tasks. Full definition
It featured a slightly improved processor and support for a 32 GB SD Card. (goodereader.com)
It includes a ton of incremental features: dual - camera, improved processor speeds, water resistance and a new home button. (thenextweb.com)
Of course, one of the big points to note with all of these units, is that they come with much improved processors compared to previous streaming devices and this is an area in which you will need good performance. (androidheadlines.com)