When you bisect something, you cut it into two equally sized pieces. (from Latin: "bi" = two, "sect" = cut)
Bisecting an interval creates two smaller intervals each with half the length of the original interval. Some examples:
• bisecting [0, 2] gives the intervals [0, 1] and [1, 2]
• bisecting [-1, 1] gives the intervals [-1, 0] and [0, 1]
• bisecting an arbitrary interval gives the intervals
and