This is Tanwin or Nunation. You think of it as the English a/an marker for indefinite nouns. Tanwin as a vowel has various jobs in Arabic but at this level you can imagine it as the indefinite marker for the indefinite nouns. Thus if the word does not come with the definite article AL, it has to bear Tanwin to its end.
The last word in the sentence above, مهمة should be (muhimmatun) but because this word is at the end of the sentence, there is no need to add the last vowel, and thus it becomes (muhimmah).
Ta-Marbútah at the end of nouns, specially feminine, changes to from H to T when it is adjusted by a vowel.