The black line around the gums is calcified Plaque which is called Calculus which has become accumulated around the tooth. Its basically deposition of bad oral bacteria which infects the tooth and gums.
The solution is get it removed immediately othervise it will progress further and will weaken the gums and tooth.
Next Steps
You must get proffessional full mouth cleaning done from the dentist. It is called Dental Scaling in medical terms.
Health Tips
Brush twice daily, avoid sugary foods, use mouthwash after brushing, do warm saline rinses daily after meals.