The Precautionary Principle was initially proposed in the Declaration on Environment and Development at the United Nations Conference in Rio de Janeiro in 1992 and states that,
"In order to protect the environment, the precautionary approach shall be widely applied by States according to their capabilities. Where there are threats of serious or irreversible damage, lack of full scientific certainty shall not be used as a reason for postponing cost-effective measures to prevent environmental degradation."
In other words, when considering actions (or inactions) whose consequence could pose serious or irreversible damage to human health or the environment, the burden of proof that those actions won't cause harm lies with those taking the action. The Precautionary Principle affords policy makers discretion in the decision making process when there's the possibility of causing harm, but not the extensive scientific research to substantiate that risk.
There are two broad types of the Precautionary Principle - strong and weak.
In the strong version of the principle, costs are not considered in preventative action, and no level of environmental risk is acceptable, regardless of the economic or social benefits. A strong precautionary principle may also involve a mechanism by which those advocating for the action to be taken (and claiming its environmental / human health risks are nonexistent or low) are liable for any environmental harm that may result.
With a weak precautionary principle, there must be some evidence to suggest a given likelihood and severity of environmental harm. A weak precautionary principle takes into account the costs of precautionary measures as well as the benefits vs costs of such actions. In addition to scientific uncertainty, economic considerations can postpone action. The burden of proof falls on those advocating for the precautionary action, and there's no assignment of liability.