A good definition of the carbon tax can be found here:
At the centre of the government’s policy on climate change is pricing carbon. Many commentators and politicians have referred to this as a “carbon tax”. The idea is that polluters will pay per tonne of carbon they release into the atmosphere. This cost will initially be set at $23, and increase gradually until 2015, when we will shift to a trading scheme that will let the market set the cost. This is widely thought of as the most effective and least costly mechanism to reduce carbon output and reduce the level of climate change that is occurring. 
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Wikipedia describes it this way:
A carbon tax is an environmental tax levied on the carbon content of fuels.[1] It is a form of carbon pricing. …….
Carbon taxes offer a potentially cost-effective means of reducing greenhouse gas emissions.[6] From an economic perspective, carbon taxes are a type of Pigovian tax.[7] They help to address the problem of emitters of greenhouse gases not facing the full (social) costs of their actions. Carbon taxes are a regressive tax, in that they disproportionately affect low-income groups. The regressive nature of carbon taxes can be addressed by using tax revenues to favour low-income groups.[8]
One advantage of a carbon tax is that people understand the concept of a tax. Mind you, they hate it! Another advantage is that governments already have processes to collect taxes, so the bureaucracy is already there.
