This is the 8227th most frequent Turkish word.
mesleği
"Mesleği" means "his/her/its profession" in English.
Here, 'mesleği' refers to the person's specific professional career or field.
Onun mesleği doktorluktur.
His/her profession is being a doctor.
In this question, 'mesleğinizi' is the possessive form denoting 'your profession', applied here to inquire about feelings towards one's profession.
Siz mesleğinizi severek mi yapıyorsunuz?
Do you practice your profession with passion?
Here, 'meslekleri' indicates the plural possessive form, showing the general importance of professions collectively to society.