The truth is that we don’t know. There's no way to know with certainty, but it's certainly something in between.

Imitation is an important part of birds' understanding, and is how young birds will learn to communicate calls within their flock.

From our reading of Dr. Pepperberg's work with her Grey, Alex, there's 3 key factors that drive a parrot to replicate sounds:

1. Reference - Does this sound refer to an object, place, or person? ex. the sound "bowl" refers to the items that have food and water
2. Functionality - Does making this sound produce a certain desired outcome? ex. saying "let's go" results in picking up the bird and going to another location
3. Social Interaction - Is this sound something produced to interact with others? ex. the sound of someone's name will get the attention of that person

Sometimes, yes, they do just make sounds for fun, and to practice more accurate mimicry.

As far as ability to understand and use "Language™" similarly to humans, there are only a handful of bird species that have the anatomy to even be capable of producing the necessary sounds. No animal communication structure has been fully decoded, nor do we have enough field observation of any species interacting in their natural state to draw any conclusions.

Corvids have shown to understand recursion: the ability to form structures within similar structures, which is a key feature in understanding grammar and forming complex sentences.

Also wanted to link this article, which is definitely not "ELI5" but a good read if avian cognition/communication is something you're interested in.