From Envirowiki

Carbon neutral refers to any process that emits no net carbon. That is, it can emit some, then remove the same amount from the atmosphere, or vice-versa.

Carbon neutrality is most frequently used when talking about carbon offsetting, especially related to travel - many companies offer carbon neutral offsets for car driving, or flying. In reality, these schemes are nearly always dodgy, even if they are well intended. This is because the emissions being offset originate from fossil fuels, and this pretty much permanently adds carbon to the carbon cycle that wouldn't have otherwise been there. This can only be properly undone by replacing the carbon in a permanent, safe store, for example by sequestering it in soils, where it might eventually become part of the earth's crust again.

However, most carbon offset schemes are based on tree planting, which only removes carbon from the atmosphere, not the entire carbon cycle, and is only permanent if the resulting forest is never removed again, and is often fraught with problems of accounting and accountability. Other schemes offer things like energy efficiency savings, but these may have been going to happen any way (see for example the European Union ETS), or they offer investment in renewable energy. The latter option can be a good one, as it will have an impact on future emissions, but it won't remove the emissions from the atmosphere, so it can't be said to be truly carbon neutral.