When coherent waves overlap each other, there is superposition of waves in which the resultant displacement is the algebraic sum of the individual displacements. This overlap may cause the resultant wave to increase or decrease.
If the waves are out of phase to one another, i.e. in 180 degrees then the two waves cancel each other out and the resultant wave is zero. This is destructive interference.
If the waves are in phase i.e 0 degrees or 360 degrees then the two waves create a wave with bigger amplitude. This is constructive interference.
So, when seen in the screen, interference pattern is formed consisting of dark ( in the case of destructive interference)and bright( in case of constructive interference) fringes are formed.