This is the 1563rd most frequent Polish word.
dużego
"Dużego" means "big" or "large" in the genitive or accusative singular masculine form or genitive singular neuter form.
In this sentence, 'dużego' is used as an adjective modifying 'kota', and it is in the masculine genitive singular form, agreeing with the noun.
Widzę dużego kota.
I see a large cat.
Here, 'dużego' is again an adjective describing 'psa', in the masculine genitive singular to match the noun following the preposition 'z'.
Nie boję się dużego psa.
I am not afraid of the large dog.
'Dużego' is used to describe 'stołu', which is masculine and in the genitive case due to the preposition 'z'.