incenter
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The point in a triangle where all three angle bisectors meet is called the incenter.
In short, the orthocenter really has no purpose. There are 4 points of Concurrency in Triangles: 1) The Centroid - the point of concurrency where the 3 medians of a triangle meet. This point is also the triangle's center of gravity. 2) The Circumcenter - the point of concurrency where the perpendicular bisectors of all three sides of the triangle meet. This point is the center of the triangle's circumscribed circle. 3) The Incenter - the point of concurrency where the angle bisectors of all three angles of the triangle meet. Like the circumcenter, the incenter is the center of the inscribed circle of a triangle. 4) The Orthocenter - the point of concurrency where the 3 altitudes of a triangle meet. Unlike the other three points of concurrency, the orthocenter is only there to show that altitudes are concurrent. Thus, bringing me back to the initial statement.
The point of concurrency (intersection) of 3 perpendicular bisectors (the lines that cut the sides of the triangle in half at a 90 degree angle...think of a plus sign--+) of a triangle. It's equidistant to the 3 vertices (points or ends) of the triangle.
the point where the three angle bisectors of the triangle intersect
The angle bisectors of a triangle are the lines which cut the inner angles of a triangle into equal halves. The angle bisectors are concurrent and intersect at the center of the incircle.