explain why government spending on infrastructure and training programmes for the unemployed are examples of investment expenditure

Government spends money for a variety of reasons, including: To supply goods and services that the private sector would fail to do, such as public goods, including defence, roads and bridges; merit goods, such as hospitals and schools; and welfare payments and benefits, including unemployment and disability benefit.

Spent on thing like Federal expenditures fall into five main categories: health insurance (Medicaid and Medicare), retirement benefits (Social Security), national defense, interest on the debt.