From your description, it does sound like your Parrot has some understanding of meaning, much like dogs do. Not that they understand the grammar or can make out

From your description, it does sound like your Parrot has some understanding of meaning, much like dogs do. Not that they understand the grammar or can make out the individual words, but it seems like it can correlate <real world event> with <sounds>. <get back up> -> "Good boy"; <caught you right where I wanted you> -> "<snap> + Ah-ha!". Similarly, a dog may not understand that "sit" is an English word, but it can clearly understand "sit" -> <get that ass on the floor> (or whatever language you used to train them, they couldn't care less). That association is meaning, even if they are not fully acquainted with the works of Shakespeare.