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This paper presents BigEarthNet that is a large-scale Sentinel-2 multispectral image dataset with a new class nomenclature to advance deep learning (DL) studies in remote sensing (RS). BigEarthNet is made up of 590,326 image patches annotated with multi-labels provided by the CORINE Land Cover (CLC) map of 2018 based on its most thematic detailed Level-3 class nomenclature. Initial research demonstrates that some CLC classes are challenging to be accurately described by considering only Sentinel-2 images. To increase the effectiveness of BigEarthNet, in this paper we introduce an alternative class-nomenclature to allow DL models for better learning and describing the complex spatial and spectral information content of the Sentinel-2 images. This is achieved by interpreting and arranging the CLC Level-3 nomenclature based on the properties of Sentinel-2 images in a new nomenclature of 19 classes. Then, the new class-nomenclature of BigEarthNet is used within state-of-the-art DL models in the context of multi-label classification. Results show that the models trained from scratch on BigEarthNet outperform those pre-trained on ImageNet, especially in relation to some complex classes including agriculture, other vegetated and natural environments. All DL models are made publicly available at http://bigearth.net/#downloads, offering an important resource to guide future progress on RS image analysis.