Direct taxes are taxes that are directly paid to the government by the taxpayer. These taxes are applied on individuals and organizations directly by the government. E.g. Income tax, Corporation Tax, Wealth Tax, etc.
Indirect taxes are those applied on the manufacture or sale of goods and services. These are initially paid to the government by an intermediary, who then adds the amount of tax paid to value of the goods / services and passes on the total amount to the end user. Examples : Sales tax, service tax, excise duty.