As of now, no entity is required to become CO2 neutral, although more and more regulations are taking shape that limit the amount of CO2 emissions an entity can generate, such as the cap and trade system, building energy codes, etc.
"Although no one is paying right now, it is clear that every emission does have its costs for society in terms of future, adverse climate impacts. A company/organisation that voluntarily achieves carbon neutrality chooses to take full responsibility for its emissions by internalising those CO2 emissions."
Whereas energy efficiency measures often provide cost savings for an entity, carbon offsetting comes with a cost without apparent direct return. However, with the increasing importance of corporate social responsibility (CSR), commitments to sustainability and social equity such as carbon offsetting can, among other benefits, help attract new customers and increase staff motivation. Therefore some companies and organisations decide to offset their remaining emissions voluntarily in order to become CO2 neutral. In addition, an increasing number of environmentally conscious individuals are opting to offset certain CO2 emitting parts of their lifestyle, e.g. buying CO2 offsetting credits when taking a flight.
The voluntary aspect of this carbon offsetting is important, because this voluntary offsetting should be distinguished from the offsetting and trading of carbon credits taking place in the so-called compliance carbon market that has come about as a result of the ratification of the Kyoto Protocol and, more recently, the EU Emission Trading Scheme. The credibility of the compliance market has been dented due to large scale abuse, over-allocation of emissions rights, and an unanticipated oversupply of credits through the financial crisis of 2008.
The voluntary carbon market on the other hand is less influenced by these problems, is much smaller, and is less aimed at energy intensive emitters. More information on the voluntary carbon market and the compliance carbon market and their differences can be found here