A constitution is not needed by the country, but rather by its population. To understand how and why it is needed, we must harken back to the "olden" Roman times (archaism intentional, purely for stylistic purpose).
Rome, like most ancient civilisations, did not have written laws. Whenever there was any dispute, the Senate, formed by the elderly patricians, was called to action. This was a very conservative system, not only were the Senators elderly and not elected, but they were members of the upper class. Their role was to know, interpret and apply "customs" when the dispute must be settled. This was a tremendous power, that they could use almost at whim to assert the privileges of the upper class when patricians and plebeians (the people) were in dispute.
But as literacy spread (why do I remember McLuhan so often?), the plebeians came up with the idea that they wanted those "customs" written down. This claim is revolutionary because it implies two things:
That the people wanted to know the law they had to obey. Knowing the law gives you, in theory, the power to avoid punishment for breaking it. They didn't want the law to be amended, changed or forgotten as the Senators saw fit. Fixing the law into written form meant to revoke the indiscrimnate jurisprudential power from the Senate. Here it was born the concept of clear separation between legislation and justice. Soon after the "Twelve Tables" were written, plebeians noticed that the laws were very strict and biased against the people. They then started to work towards changing them. Thus we know the two main reasons why written laws are desirable:
Known laws can be evaluated as good and bad, noxious or beneficial, and improved or revoked. As the written law supersedes tradition, changes can be effected by editing the text, instead of waiting for the customs to change.