A level playing field is a concept about fairness, not that each player has an equal chance to succeed, but that they all play by the same set of rules. A metaphorical playing field is said to be level if no external interference affects the ability of the players to compete fairly. Although some may view "government interference" to slant the field in reality the level playing field is created and guaranteed by the implementation of rules and regulations ... building codes, material specifications and zoning create a starting point/ a minimum standard --- a "level playing field".
Examples where governments, regulators and sports associations have tried to create a 'level playing field':
(Education) Students who have parents with low incomes can be considered for a scholarship so they are able to study at a university. (opposite of a handicap; see below)
(Business in general) Every company within the same branch is obliged to pay the same percentage of tax over their annual income to the government every year.
(Banking Business) Every bank is in need of a banking licence to be allowed to sell banking products to consumers and retailers. You can not just start your own new bank without permission of the financial regulators within your state.
(Car Industry) Every car manufacturer has to make sure that the car he puts on the market is "safe" drive in. You can not sell cheap cars and make a lot of money without guaranteeing to consumers that the car is safe while being used on the road.
(Sports) When playing football every team is allowed to let the same amount of people participate in the game and on the field.
(Sports) Ski jumpers all jump from the same height when jumping off of a rail.
(Sports) Formula 1 cars and there drivers all have been submitted to the same set of rules before participating a race. Even the combination of the weight of the car and driver has been corrected and made equal in relationship to their opponents.
Handicapping might be thought of as the opposite concept, of unequal rules designed to make the outcome of play more equal.