In common usage, saving generally means putting money aside, for example, by putting money in the bank or investing in a pension plan.
In economics, saving is specifically defined as income minus consumption. In other words, income that is not consumed by immediately buying goods and services is saved.
Saving in economics is not always the same as what people normally mean by saving. For example, the part of a persons income that is spent on mortgage repayments is not spent on present consumption and is therefore saving by the above definition, even though people do not always think of repaying a loan as saving.
Saving is closely related to investment. By not using income to buy consumer goods and services, it is possible for resources to instead be invested by being used to produce capital, such as factories and machinery. Saving is therefore vital to increase the amount of capital available, which contributes to economic growth.