Upgrade does, generally, mean to make something you already have better. You can upgrade your computer, and that fits clearly in that understanding.
However, it can also apply to the role that object plays for you. If you already have a phone, and replace it with a better phone, that is an upgrade of "your phone", even though it's not an upgrade of the actual device in question.
People will also talk about upgrading their cooker, their TV - even their car, where upgrade could mean having some part of the car replaced with a better version, like upgraded wheels - but it could also mean just getting a better car.
Some people also use this language about romantic partners, which is kind of unpleasant.
The important point is that you wouldn't use it for getting something you don't already have, or getting a second (or third) while you still use the old one. You also only use it if the new one is better. If it's a like-for-like replacement, it's not an upgrade.
(Though on that last point, the process of "upgrading" a mobile phone as an incentive from a phone company can sometimes lead to a near enough like-for-like replacement being called an upgrade.)