Learn Turkish: Bu büyüyü kimse fark etmedi.

Büyü means "spell" or "magic". Because we are talking about a specific spell ("this spell"), it needs the definite accusative case to show it is the direct object of the verb. The -y- is a buffer letter to separate the two vowels, and -ü is the accusative suffix following vowel harmony rules.

Kimse means "nobody", so why is the verb negative (fark etmedi)?

In Turkish, words like kimse (nobody/anybody) or hiçbir şey (nothing/anything) require a negative verb when they are used to mean "nobody" or "nothing". The negative suffix here is the -me- in fark et-me-di. It literally translates to "Nobody didn't notice this spell."

How does the verb fark etmek work?

It is a compound verb made of the noun fark (difference) and the helper verb etmek (to do / to make). Together they mean "to notice" or "to realize". When you conjugate compound verbs like this, you only add the suffixes to the helper verb, which is why it becomes etmedi.

Why does this sentence use the definite past (-di) instead of the reported past (-miş) from this lesson?