To an extent, you're right. The Harrod-Domar model of development suggests that the amount of growth of an economy depends on the savings ratio over the capital output ratio.

The reason for that is a bit mathematical, so bear with me:

When Savings = Investment (assuming for simplicity, no foreign trade)

  S=I (1)
  now S=sY (2), 

where little s is the savings ratio, and big Y is GDP (output), and

  I=ΔK,

which is to say investment is the difference in capital stock (which is the definition of investment).

  ΔK=k.ΔY

where little k is the capital output ratio (amount of output produced per change in capital),

  so I=k.ΔY (3).

Substituting (2) & (3) into (1) gives you:

  sY=k.ΔY

rearranging gives you

  ΔY/Y = s/k

or in other words, the rate of growth of GDP depends on the propensity of an economy to save, and then how much of that saving goes into output.

So in a sense, you're right, but there's more to it than that.

The problems occur when there's too much hoarding going on. Think of these two theoretical extremes:

1) Everyone saves, no-one spends. (Leaving aside starvation and human needs for the moment)

- Obviously, since no-one spends anything, no-one ever gets paid. No transactions happen at all, and interest rates drop (no-one's borrowing anything!) so people suffer, and experience poorer standards of living as a result. There's a lot of money, but no-one's doing anything with it.

2) No-one saves at all, and everyone spends what they earn relatively quickly

- In comparison to 1), this would mean that you're likely to be being paid a lot, and quicker. You immediately spend this money on goods, so your quality of life (in theory) increases immediately. It doesn't matter that you don't have the money any more, as the next person along that you spent your money on also immediately spends their money. Money travels around fast (the speed of which it does this is known as the velocity of money), and so you're soon being paid more money again, which again improves your quality of life. No saving takes place - but no-one minds as there's so much money going around that bootstrapping a business suddenly becomes a lot easier.

Obviously, 2) is unfortunately rather impossible to achieve - due to various factors such as confidence and the difficulty in getting everyone to spend lots. One noted problem is that rich people spend more money than poor people - but they spend a smaller proportion of their income. Imagine someone with £100,000 pa (after tax). They spend say, 20% of their income at £20,000 a year. Now imagine someone earning a paltry £10,000 pa (after tax). They're likely to spend a higher proportion of their income, say 80% at £8000 a year. 10 of these poorer people will spend £80,000 a year. So the theory goes, it's better to have more people all spending and increasing the velocity of money, than a few very rich people all hoarding.

In the real world, savings matter, because you can't get everyone to spend lots of money all the time. However, these savings accounts can't be high enough to jeopardise spending. It's a bit of a tightrope.