What is a reversible process?
The process that has no effect on the surroundings, when it undergoes in either (forward or backward) direction is called the reversible process. In this process, the net heat and net work interaction between system and surroundings is zero for combined (forward and backward in time) processes.
It is like watching a video clip in the forward and reverse direction and no one can tell which one is reversed.
A reversible process is an idealized concept and no process in nature that happens spontaneously is reversible. Every process that occurs in nature is irreversible.
The laws of electricity and magnetism, the law of gravitation, the law of conservation of energy, and momentum all work exactly similarly in the reverse direction. But in reality, there is always the presence of irreversibilities like friction that cause this to not happen.
What is an irreversible process?
The process which can leave some kind of trace on the surroundings is called the irreversible process. There is always some kind of net heat or net work interaction between the system and surroundings. Irreversible processes are spontaneous processes and occur naturally. Everything that happens in the real world is irreversible and has a net effect on the surroundings directly or indirectly. Although some processes can occur in a reverse direction according to the laws of physics, they don't happen spontaneously in the reverse direction even if we wait for million years. Nature always follows a certain direction for processes and even though it is possible for the process to happen in the reverse direction reversible process simply does not occur.
What is the significance of reversible process over irreversible process?
The reversible process tells us about the theoretical limit of the net output of processes. That is it tells us what could be the maximum possible work extracted from work producing devices(engines/turbines) or what could be the least possible work consumption in the case of work consuming devices (refrigerators, heat pumps) if these processes undergo in a reversible manner.
Reversible processes are easy to analyze as well as they make it easy to compare net outputs of devices with irreversibilities.