When deciding a particular case, judges will be attentive to the decisions made by other judges in similar cases. These judgements are called 'precedents'. Some precedents will be binding on a particular court; for example, a decision of the Court of Appeal cannot easily be overridden by lesser courts if the circumstances of the case are similar (see: Stare decisis). Of course, the judge has some flexibility in deciding how similar a current case is to precedent. Note that only the ratio dicidendi of a judgement -- that is the decision actually made and its reasons (see: Ratio dicidendi) -- is binding, not points discussed as an aside (see: Obiter dicta).
Some precendents may be 'persuasive', but not binding. Persuasive precedents include rulings of the Privy Council, and some Commonwealth and US courts, and statements made obiter dicta in earlier judgements.
It is probably fair to say that the principles of binding precedent are applied more strictly in civil, rather than criminal, cases.