Importing means to place a product from a third country on the market or into service. Importing is done by importers of which the RCD 2013/53/EU defines two types of actors:

‘importer’ means any natural or legal person established within the Union who places a product from a third country on the Union market.

‘private importer’ means any natural or legal person established within the Union who imports in the course of a non-commercial activity a product from a third country into the Union with the intention of putting it into service for his own use.

Both types of actors must act with due care and ensure that the product is in conformance with the requirements of the RCD 2013/53/EU. Typically, a manufacturer will assume responsibility for the conformity of the product. In cases that the manufacturer has not taken such steps and the product does not possess conformity with the RCD 2013/53/EU the importer and private importer must ensure that it has been designed and manufactured in accordance with the essential requirements set out in annex 1 of RCD 2013/53/EU. Importers and private importers must draw-up and keep technical documentation for 10 years in the case that the manufacturer has not taken responsibility for the conformity of the product. When engaging in importing activities all actors must ensure that the product is accompanied by instructions and safety information in the owner’s manual. If a national authority requests documentation proving the conformity of the product importers and private importers must prove this within a reasonable timeframe.

Additionally, an importer must ensure that while a product is under their responsibility, storage or transport the product's compliance is not jeopardised. When deemed appropriate with regard to the risks presented by a product, importers shall, to protect the health and safety of consumers, carry out sample testing of products made available on the market, investigate, and, if necessary, keep a register of complaints, of non-conforming products and product, recalls, and shall keep distributors informed of such monitoring

Importers shall indicate their name, registered trade name or registered trademark and the address at which they can be contacted on the product or, where that is not possible, on the packaging or in a document accompanying the product.

For the full text & explanation please read RCD 2013/53/EU chapter II, detailing obligations of various actors including importers.