Over the past years, Semantic Web and Linked Data technologies have reached the backend of a considerable number of applications. Consequently, large amounts of RDF data are constantly being made available across the planet. While experts can easily gather information from this wealth of data by using the W3C standard query language SPARQL, most lay users lack the expertise necessary to proficiently interact with these applications. Consequently, non-expert users usually have to rely on forms, query builders, question answering or keyword search tools to access RDF data. However, these tools have so far been unable to explicate the queries they generate to lay users, making it difficult for these users to i) assess the correctness of the query generated out of their input, and ii) to adapt their queries or iii) to choose in an informed manner between possible interpretations of their input. This paper addresses this drawback by presenting SPARQL2NL, a generic approach that allows verbalizing SPARQL queries, i.e., converting them into natural language. Our framework can be integrated into applications where lay users are required to understand SPARQL or to generate SPARQL queries in a direct (forms, query builders) or an indirect (keyword search, question answering) manner. We evaluate our approach on the DBpedia question set provided by QALD-2 within a survey setting with both SPARQL experts and lay users. The results of the 115 filled surveys show that SPARQL2NL can generate complete and easily understandable natural language descriptions. In addition, our results suggest that even SPARQL experts can process the natural language representation of SPARQL queries computed by our approach more efficiently than the corresponding SPARQL queries. Moreover, non-experts are enabled to reliably understand the content of SPARQL queries.