"The girl is playing."
Translation:Das Mädchen spielt.
I think it helps to distinguish between biological sex and grammatical gender. In German, the biological sex of people and the grammatical gender of the corresponding nouns generally coincide, e.g. a man is male and the noun "der Mann" is also grammatically masculine.
There are some exceptions, though, and one of them is "das Mädchen". Of course a girl is biologically female, but the noun "das Mädchen" is grammatically neuter. The reason for this is that all nouns ending in the suffix "-chen" are automatically assigned the neuter gender.
Etymologically, the word "das Mädchen" developed from "die Magd", which at one time meant "unmarried woman, virgin", and the suffix "-chen", which means "little". So originally, the word for girl meant "little unmarried woman". To make it easier to pronounce, "das Mägdchen" finally became "das Mädchen".
Here is what Mark Twain had to say on the subject, by the way :)
"In German, a young lady has no sex, while a turnip has. Think what overwrought reverence that shows for the turnip, and what callous disrespect for the girl. See how it looks in print - I translate this from a conversation in one of the best of the German Sunday-school books:
"Gretchen. Wilhelm, where is the turnip?
Wilhelm. She has gone to the kitchen.
Gretchen. Where is the accomplished and beautiful English maiden?
Wilhelm. It has gone to the opera."