"The eagle is eating a mouse."
Translation:Ο αετός τρώει ένα ποντίκι.
το is the neuter definite article, used before neuter nouns.
ο is the masculine definite article, used before masculine nouns.
η is the feminine definite article, used before feminine nouns.
Which noun belongs to which gender is something you have to learn, though you can often tell from the ending.
In the accusative case, though, the masculine article becomes τον and the final nu is sometimes dropped, giving το (e.g. βλέπω το σταυρό where ancient Greek would have τον σταυρόν).