The two overlap: Bookkeeping is part of accounting. It is the recording of the day to day transactions of a business.
Therefore, bookkeeping can play an important role in the efficient running of a business: A business needs to pay its bills and it must therefore keep a record of those bills so that the correct amounts can be paid at the correct times and also so that bills are not paid twice by mistake. Similarly, a business needs to keep track of cash and cheques received from customers. Generally, all these things are the concern of bookkeeping.
Accounting builds on the bookkeeping information, interpreting it, compiling reports, year-end accounts, tax returns, budgeting and carrying out financial analysis and so on.