Boundary conditions are constraints--e.g. displacements, forces, pressures, velocities, temperatures, etc.--imposed on the edges or surfaces of a system. They are used to solve mathematical models of physical systems, including those used in computational methods like finite element analysis.
A cantilever beam has clamped-free boundary conditions at its ends. The other boundary conditions change its behavior: gravity loading or another downward force applied to the top surface causes bending, whereas a compressive axial load at the free end can lead to buckling.