The Volcker Rule is, in the text of the statute, section 13 of the Bank Holding Company Act. Section 619 of the Dodd-Frank Act added it1. In the rule, the funds subject to the prohibition are called "covered funds"2.
After the prohibition, the statute lists underwriting, market making, risk-mitigating hedging and other activities as permitted activities. The scope of the prohibition is set by the definition of a banking entity, the definition of the trading account, and the requirements for permitted activities. The details are covered in related articles.