What does depeche in the passage mean?

Emily, 

the verb is the reflexive expression ‘ se dépêcher de ( faire qqc) ‘. 

Do you know you can get the translation of phrases in the exercise by clicking on them? There are also many good online dictionaries - bilingual or monolingual as needed - to check words and many expressions eg wordreference, Larousse, Robert etc 

‘ Se dépêcher de m’habiller … ’ here  ‘ I hurry getting dressed … ‘  is the translation given in the exercise 

 https://www.wordreference.com/fren/d%C3%A9p%C3%AAche

to hurry up

to hurry