The payments on account are based on the last tax year and the balancing payment is the difference in the payments you have made so far based on the last tax year and your actual assessment. e.g. say your payment on account for year 2009/10 were £4,000 so your payments on account for the next year 2010/11 will based on that figure £4,000 and the payments will be:
31 January 2011 £2,000 31 July 2011 £2,000
Now, if your tax assessment for the year 2010/11 came to, say, £5,700 then your balancing payment will be £1,700 and you have paid all the tax you had to. Hope it makes sense?