Hire purchase is a way of getting goods on credit but, unlike most other forms of credit, you don't own the goods until the final payment is made. (So, while you're making payments, you're 'hiring' the goods but, at the end of the contract period, you complete the purchase of them).
When I was a child (around half a century ago!), HP was the only way that 'the man in the street' could obtain credit. With the introduction of credit cards and other credit arrangements (where the purchaser owns the goods immediately but takes on a loan to pay for them), HP became less popular and almost ceased to exist. However, car manufacturers have re-introduced HP schemes as a way of purchasing cars. (Unlike the original HP schemes, those offered by car manufacturers require a substantial cash payment, at the end the hire period, to complete the change from 'hiring' to 'purchasing' the vehicle).
See here for general information about HP agreements:
http://www.oft.gov.uk/shared_oft/consumer_leaf lets/credit/oft809.pdf
See here for information about what happens if you get into debt with an HP agreement:
http://www.direct.gov.uk/en/MoneyTaxAndBenefit s/ManagingDebt/DebtsAndArrears/DG_10013226
Chris