What are hiding under these letters? What do they stand for? I have read many others, but I could never understand what they mean and the pilot's career on each of them. If possible, can anyone post a brief list and their tasks and responsibilities, please?
PPL is Private Pilot License
May fly for pleasure or personal business. Private pilots cannot be paid, compensated to fly, or hired by any operator.
CPL is Commercial Pilot License
Can be paid, compensated to fly, or hired by operators and are required to have higher training standards than private or sport pilots.
ATPL is Airline Transport Pilot License
ATPs, as they are called, typically qualify to fly the major airliners. ATPs must qualify with a range of experience and training to be considered for this certificate.
Nobody has mentioned experience specifics.
You can get a PPL in about 35 flying hours. It is really a licence to learn how to fly, but without being paid to do so.
You can get a CPL in about 250 flying hours. This also is a licence to learn how to fly, but while being paid to do so. This is also much more difficult to earn, involving much higher precision flying and a ton more knowledge.
You can get an ATPL in about 1,500 flying hours. It is a licence that tells professional pilots you have now learned the basics of how to fly an airplane.
Having said that, a pilot never stops learning, every type they add requires extensive training, and MOST commercial pilots come close to killing themselves about five times during their career.
Commercial pilots also have to prove they still have their skills - and their health - every six months.
ATPL, 13,600 hours.
PPL is a "Private Pilots License" and is a qualification which allows you to act as Pilot in Command in an aeroplane [PPL(A)] or Helicopter [PPL(H)] without remuneration. It is the most common license held in general aviation, and is the first step to all the other licenses that you mentioned in your question.
CPL is a Commercial Pilots License, and allows you to act as Pilot in Command of a charter or corporate flight.
ATPL (or ATP Certificate) is an Airline Transport Pilots License and is the highest level of pilot certification.
Private Pilot License. You may fly your own plane or rent one to fly. You can fly families and friends. You can not be paid to fly.
Commercial Pilot License. You can be paid to fly, but usually in small planes only. Typical activities include aerial photography, banner towing, dropping sky divers, etc.
Airline Transport Pilot License. You can act as captain of a large airliner.
To give a rough perspective, PPLs usually fly small single-engine propeller planes; CPLs fly slightly larger planes that carry maybe 20~50 people, ATPLs are the ones that fly Airbus and Boeings.
Note that the pilot license restricts which kind of aviation activity a pilot can fly, but does not restrict the size or speed of the aircraft. Technically you can fly an A380 with a PPL if you fly it privately, but very few people (if any!) do that.
In the simple sense, PPL must be acquired before CPL, and CPL before ATPL. It is like driving licenses: you must get an ordinary driving license before you can drive a bus, and you better can drive a bus before you want to drive a semi-trailer. The higher privilege licenses require better precision, better proficiency and handling more complex aircraft systems.
Obviously, pilot and driving licenses vary country by country, but I feel this answer address the OP's concerns.