A society, or even a person or household, gets richer by saving. It would be very difficult, or perhaps impossible, for a society to get richer if everyone consumed everything and saved nothing. The same generally holds true for a person or household, although someone could make a higher income and have a higher standard of living (at least as long as the higher income lasted) without saving anything.
Savings is required for capital investment. Capital investment is what leads to better production and better technology. In an advanced society, it leads to higher wages, lower prices, and an overall higher standard of living.
If someone were stranded on an island alone, let's say he could catch two fish every day. It took him from sunrise to sunset to catch just two fish. At sunset, he had to go into his cave and sleep and stay safe from wild animals. If he always consumed two fish every day, then he would never get ahead.
Let's say the guy on the island consumed only one fish per day and found a way to preserve the second fish he caught. The next day, instead of fishing, he might have some time to build a better shelter. He wouldn't need to fish the whole day, as he would be able to eat from his prior savings. The guy could also spend a day building a fishing net. This might help him catch 4 fish in a day, instead of just 2. The fishing net is capital investment. He was able to make it because of his prior savings (a fish). He deferred consumption of a fish so that he could build a net. Through savings and capital investment, he has increased his productivity. Now he can fish for just half a day, consume two fish, and still have time to do other things.
Some people who don't understand economics, finance, and even math, think that if you save some money, that you will always have a lower standard of living until you tap into that savings. They don't understand the benefits of compounding interest.
Henry Hazlitt made a point similar to this in his classic book Economics In One Lesson.
If you make $100,000 per year (after taxes for the sake of this argument) and you always save 10% of your income, let's see what happens. The first year you save $10,000 and you spend $90,000.
The second year, you still make $100,000 and you save $10,000 again. But let's also say that you make a 5% return on your initial $10,000 that you saved last year. So you actually made an extra $500 or $100,500. You could simply decide to consume 90% of the $500 and continue to save 10%. So your consumption in year two would actually be $90,450 and your savings after year two would be $20,050 ($10,000 in savings for two years, plus $50 saved from your first year returns).
If this situation continues, then eventually your consumption will be over $100,000, while the savings continue to add up. By deferring consumption, you are actually able to have a higher standard of living than when you started off, even if you had consumed everything in the first year.
Of course, you could save even more aggressively and consume less of your return, which in this case starts out at $500. Once you get your total savings up to $200,000, then just a 5% return would be enough to make up for the $10,000 in income that you save each year. At that point, you could consume the full $100,000 you earn each year and your savings would continue to grow just from the interest.
While interest rates are currently very low, there are still ways to get a positive return on your savings. The magic of compounding interest has not gone away. It is a wonderful thing. Compounding interest is what enables many people to get wealthy and it also enables societies to get wealthier.