Private investment, from a macroeconomic standpoint, is the purchase of a capital asset that is expected to produce income, appreciate in value, or both generate income and appreciate in value. A capital asset is simply property that is not easily sold and is generally purchased to help an investor to generate a profit. Examples of capital assets include land, buildings, machinery, and equipment.
Investment is not the same as savings in the world of macroeconomics. If you are not purchasing a capital asset that is used to generate income, such as a machine, or with the expectation that it will appreciate in value, like a house, then you are saving, not investing.
You can save more than you invest, such as when a business purchases equipment with part of its profit and puts the rest of the profit in a savings account.