Savings result from the passive activity of delayed consumption. That delay might be brief, in which case savings becomes relatively unimportant. More extended delays and consumption allow for you important developments in an economic system.
Savings allow our friends the hunters and gatherers to survive harsh winters. More extended savings allow for what we refer to as investment, which create production goods that increase future production.
Savings also provide a source of goods used for exchange, a topic that I will discuss in much further detail elsewhere.