Why is the entity concept so important to accounting?

The idea here is that the financial transactions of one individual or a group of individuals must be kept separate from any unrelated financial transactions of those same individuals or group.

The best example here concerns that of the sole trader or one man business: in this situation you may have the sole trader taking money by way of 'drawings': money for his own personal use. Despite it being his business and apparently his money, there are still two aspects to the transaction: the business is 'giving' money and the individual is 'receiving' money.

So, the affairs of the individuals behind a business must be kept separate from the affairs of the business itself.