A line which bisects an angle of a triangle is called an angle bisector of the triangle. Since a triangle has three angles, you can draw three angle bisectors in it.
Angle bisectors of a triangle pass through the same point, that is they are concurrent. The point of concurrency I is called the Incentre of the triangle.
Taking I as the centre and IL as the radius, you can draw a circle touching all the three sides of the triangle called Incircle of the triangle. I being the centre of the incircle is called the Incentre and IL, the radius of the incircle is called the inradius of the triangle.
The incentre always lies in the interior of the triangle.