Two meanings: (i) a promise as in a “contractual undertaking”; or (ii) in European law, especially competition, a synonym for a business, partnership, sole proprietorship, enterprise or company used in Articles 101 and 102 TFEU.
The European Court of Justice held in Höfner & Elser v. Macrotron that “the concept of an undertaking encompasses every entity engaged in an economic activity, regardless of the legal status of the entity or the way in which it is financed.” An undertaking is a “concept not necessarily identical with the notion of corporate legal personality in national commercial company or fiscal law.” Pre-insulated Pipe Cartel  OJ L24/1, para 154. It is not necessarily coterminous with the legal entities – so subsidiaries may be treated as a single undertaking with their corporate parents, joint ventures may be treated as separate entities or common entities of their parents, etc., and agent may be treated as a separate undertaking from its parent – or as a common undertaking, depending on the nature of the relationship.
To take the example of a parent/subsidiary relationship, the ECJ has held that they should be treated as a single undertaking if the subsidiary(its) “enjoys no economic independence” or if corporate structure “form[s] an economic unit within which the subsidiary has no real freedom to determine its course of action on the market.”
Whether parties form separate or common undertakings is important in two ways. First, fine levels set by the EU are based on the global turnover of the undertaking – thus the whether the calculation is based on the overall turnover of an entire corporate group as opposed to a subsidiary can be very significant. Second, coordination of behaviour between separate undertakings may raised cartel-like problems under Article 101.