Emission trading refers to the trading of allowance for harmful emissions between states, nations or companies.
The idea is that a central authority will grant an allowance to these entities based upon a measure of their need (for example an allowance to a country based upon total population). If a given country does not need all of their allowance, they may offer it for sale to another country that has insufficient allowances for its emission production.
The total of all allowances issued will be adjusted to keep in-line with an agreed reduction rate for the particular emission or pollutant. Thus, the central authority may control the emissions, and allow market forces to encourage countries to produce less of the emissions.
For example, less developed countries with relatively high populations, and lower pollution per head than western countries may sell their allowances to the industrialised west. However, as the supply is finite, the more that the west produces, the more that the additional allowances will cost them, until it becomes uneconomic to pollute, and more economic to convert to less environmentally harmful technologies.