Keynesian traps and flooding the building
A very rough and brutal sketch of Keynes' classical account of the savings trap is that if people save too much, rather than consume, then the velocity of money drops, inventory builds up, growth falls (and even goes negative) as businesses cut back on production. A standard account of the liquidity trap by Krugman is here.
How does the Phillip's device help? Well, it points out a truth that is often hard to see, namely that money can only be created or destroyed by the central bank. Credit cannot be 'created' without funding; money cannot disappear. These days, rather little money is stored in mattresses or bank vaults: most of it is in the form of bank deposits, securities, or other investments. And of course those assets are someone else's liabilities, i.e. funding for them. Thus these days your choice is not between putting your cash under the bed and spending it: it is between putting it in a bank - which will lend it to someone else - and spending it. In this sense saving is not quite as bad as in the classical Keynesian account, as it provides funding for corporations and individuals who do want to engage in economic activity. Even buying government bonds is not useless as the government spends the money on something.
Now of course the increase in economic activity provided by a dollar of spending on goods may be rather more than that provided by a dollar of bank deposits. But it is worth noting that the dollar of bank deposits are not useless: the bank has to do something with your money, and that something probably has positive economic value. Anything else would cause funds to build up rather too fast at the bank - something the Phillip's computer would model as water flooding out...