The laws of physics conserve information in that sense that two initially distinct states will always remain, at least in principle, distinguishable for all times, i.e. two distinguishable states A and B will never evolve into the same state C. This is equivalent to the statement that the laws of physics are time reversible, i.e. if you would end up in state C you could not tell whether the system came from state A or B.
If you, for example, start a pendulum with different initial displacements the pendulum will always end up at rest due to friction but if you could take into account the exact states of all the molecules in the air and the joint and so on you could in principle figure out in which exact positions you started the pendulum.
You could actually just very precisely measure the temperature of a pendulum in a box and infer the initial displacement from that because different initial displacements imply different initial (potential) energies and therefore different final temperatures after all the energy became thermal energy and everything in the box had time to reach the equilibrium temperature. You just couldn't figure out whether the pendulum was started to the left or to the right of the rest position with this method.
If you, for example, start a pendulum with different initial displacements the pendulum will always end up at rest due to friction but if you could take into account the exact states of all the molecules in the air and the joint and so on you could in principle figure out in which exact positions you started the pendulum.
You could actually just very precisely measure the temperature of a pendulum in a box and infer the initial displacement from that because different initial displacements imply different initial (potential) energies and therefore different final temperatures after all the energy became thermal energy and everything in the box had time to reach the equilibrium temperature. You just couldn't figure out whether the pendulum was started to the left or to the right of the rest position with this method.