Essentially a criminal offence is something for which the State can or will take action against you (i.e. by prosecuting you). Actions are (generally speaking) made criminal offences where they pose a risk to society as a whole (e.g. violent offences). The punishment is often a fine, a prison sentence, community service, etc.
On the other hand, a civil offence is something for which an individual or organisation can take action against you. Actions are (generally speaking) a civil matter where they affect rights or property; civil law in general is about settling disputes rather than punishing people. They usually (but not always) involve compensation or some other financial settlement.
Do note that a number of criminal offences are also civil offences. Examples include assault, battery, etc. Therefore, a person may be prosecuted by the State for having hurt someone (engaged in violence contrary to the State's wish to maintain the peace) and may also face a civil action from the person they hurt (in order to claim compensation for the hurt they suffered).
I hope this helps!