"The mouse is a pet."
Translation:Το ποντίκι είναι κατοικίδιο.
In this context the use of the definite article το before the word ποντίκι would change the meaning of the phrase in the same way it would change it in english. What the phrase says is that "the mouse is a pet" not a specific pet, thus no need to define it with the use of a definite article. If it were a specific pet eg. In the phrase Το ποντίκι ειναι το κατοικίδιο του Γιάννη ( The mouse is the pet of Yannis) then you would have to define the word with the use of a definite article.