Learn Spanish (Latin America): El estudiante repite el mensaje del profesor. - The student repeats the teacher's message.

Repite comes from the verb repetir (to repeat). It is a stem-changing verb. For most forms in the present tense, including the "he/she/it" form used here, the last e in the stem changes to an i. So, instead of "repete", it becomes repite.

Why does the sentence say mensaje del profesor instead of "profesor's mensaje"?

Spanish does not use an apostrophe "s" to show ownership. Instead, you have to use the word de (of) and flip the phrase to say "the message of the teacher".

Where does the word del come from?

Del is a mandatory combination of two words: de (of) and el (the). In Spanish, whenever de is followed immediately by the masculine word for "the" (el), they must combine into the single word del.

How would I say this if the student were female?

You would just change the first word to La. The noun estudiante is used for both males and females, so you only need to change the "the" before it. The masculine form is el estudiante and the feminine form is la estudiante.