"The girl sees a dog."
Translation:Das Mädchen sieht einen Hund.
Like most verbs, with sieht (sehen) you've got something doing the seeing and something being seen.
The thing doing the verb is called the subject, and in German this is in nominative case. This is the default 'grammatical flavour' that we learn words in - das Mädchen, ein Hund, etc.
The thing being done by the verb is called the object, and in German this is usually in accusative case. This is another 'grammatical flavour' that modifies some words, including ein.
English also has a difference between the subject and object: "He sees me", "I see him". You can see that although "I"/"me" and "he/him" refer to the same thing, they are different 'grammatical flavours' depending on whether they are the subject or object. German does this a lot more than English, and one of the rules is that for masculine things in accusative case you use einen instead of ein.
You can read more about it in the lesson tips & notes.