Law of conservation of energy states that energy can neither be created nor destroyed. Energy can only be conserved. Take the case of throwing a ball upwards. What are the forces that act on the ball?. One is the weight of the ball that causes it to be pulled down. The next is the upward force on the ball that is provided when the ball leaves the hand.
How far will the ball travel upwards?. This question can be answered easily by using the law of conservation of energy. When the ball is thrown up the energy it has is due to its velocity or kinetic energy. During its motion upwards the ball has both kinetic energy and potential energy. The speed or the velocity of the ball will be maximum when it leaves the hand and will be zero when it reaches the maximum height. At any point in time the velocity will reduce slowly ( this is called as retardation as opposed to acceleration where the veolocity increases continuosly). The maximum height travelled by the ball can then be determined by equating potential energy at the destination ( here Kinetic energy is equal to 0 as the ball is at rest), to the kinetic energy at the start of the motion ( here the potential energy is equal to 0).
Without the force of gravity we would not be attracted downwards to our planet and so we will be always floating upwards. The LCE can be used to make important derivations even the object that is thrown upwards does not go up in the vertical direction ( or goes in a parabolic path).
Imagine a marble that is just rolling downwards on a slope and is made to go into a circular ring, energy is conserved in this case as well. One can use the Law of conservation of Energy to determine the maximum time that the marble will be inside the circular hoop.
How are we able to walk?. We walk because of the frictional force that exists between the foot and the earths surface. If friction did not exist we would not be able to stop walking. A ball that is rolling on the floor stops at some point of time due to friction between the earths surface and the ball.
