What people save, avoiding to consume all their income, is called "personal savings". These savings can remain on the bank accounts for future use or be actively invested in houses, real estate, bonds, shares and other financial instruments.
National savings are personal savings plus the business savings and public savings. Business savings can be measured by the value of undistributed corporate profits. Public savings are basically tax revenues less public expenditure.
A tri-lateral relationship among savings, consumption, and income is the key determinant of the amount of personal savings. On the first side, given a certain income, the decision to buy goods and services (=consumption) negatively affects savings. Savings passively adjust to consumption and income. They represent a resource slack, buffering shocks in income and consumption desires.
On a second side, savings can be actively planned in binding agreements, like many pension schemes, with consumption passively adjusting to changes in income.
In other terms, savings can arise from a compulsory tendence of renouncing and postponing even banal consumption (greediness) or, instead, they can be the result of sharply rising income, with higher consumption taking place meanwhile.
By contrast, savings can be also the outcome of negative expectations about future income (as when one is afraid of being dismissed) ("Hey, family, hardships are coming - we need to reduce our absolute level of consumption").
Still another different case is the situation when a family, after having spent a lot in a consumption boom, try to brake its tendencies before (or after!) they become unsustainable. Thus, savings guidelines are expressed.
In static terms, the rich save and most poor don't. At the same time, individual behavioural rules play an important role, as a UK survey shows.
Income depends on GDP dynamics but, in a world where financial markets are more and more important and there exists a large wealth (assets), it depends also on both the yield of financial instruments and the asset prices movements (capital gains and losses).
In fact, it is likely that a large part of savings is financed by the overall yield of wealth.
National savings, in turn, are the sum of personal, business, and state savings. Business save when the do not distribute all their profits: these sums, however, are usually quite tiny on a macroeconomic scale. The states often run public deficits, so that they rather dis-save. All this would lead to the conclusion that personal savings are the largest and more important part of national savings.
But this is not the entire story: some empirical analyses have shown a negative correlation between personal savings and the state savings (public surplus). High savings rate would be counterbalanced by high deficits, whereas the reduction in public deficits would not increase by the same amount the national savings since a symmetric contraction of personal savings takes place. To the extent this relationship holds, national savings would be more stable than their components.
Cumulated and invested personal savings give rise to personal wealth stock.
Savings left in bank accounts are an important part of money. To the extent the banks decide to finance business investment with respect to the amound of deposits they received, an increase of personal savings could foster investment by the established firms. If money deposited is converted in subscription to equity in one's own firm, savings serve for personal careers and independence, again with a possible link to investment in a macroeconomic sense.
Invested in Treasury bonds, savings finance public expenditure. Invested in shares, they can directly or indirectly finance the firms. Savings can also be transfer abroad by remittances, giving rise to a new choice their between consumption and savings (e.g. in the form of purchasing an existent house or in funds for entrepreneurial activity).
Insufficient and reduced savings due to an intentional policy to promote GDP growth by autonomous consumption alone might reduce, if this policy is only weakly effective, the capability of the national economy to absorb treasury bonds, what in certain circumstances can put the country under heavy pressure by foreign creditors, if public debt is large and prevalently held by foreigners.
In United States, personal savings have dramatically fallen in the last decades. More in general, it seems to be a general tendency of reduction in savings.
When a recession begins, people hoping it represents only a short-run movement try to keep the same level of consumption, thus they reduce personal savings. When the hardships are more clearly visible and previously cumulated saving buffers are successively exhausted, the households usually adapt to lower level of consumption, trying to rebuild the buffers.
Recovery can take different shapes and have different sources. If it is based on consumption expenditure and optimistic expectations, savings will be driven down until the fastly growing income will allow both higher consumption and savings.