What exactly is a background class in a classification problem? I have heard people using the term background class in the following to scenarios: 


*

*For a class which has a very high number of instances compared to other classes in a classification problem

*Sometimes just creating a class like "others" and adding all those instances for which enough features are not available to discriminatively decide the class which they belong to. For example, in Section 2 of this paper, https://www.robots.ox.ac.uk/~vgg/publications/2015/Cimpoi15/cimpoi15.pdf (this paper deals with building features for performing texture/material recognition in images). I have quoted the particular text which talks about a background class below:

In particular, we build on the Open Surfaces (OS) dataset that was
  recently introduced by Bell et al. [4] in computer graphics. OS
  comprises 25,357 images, each containing a number of high-quality
  texture/material segments. Many of these segments are annotated with
  additional attributes such as the material name, the viewpoint, the
  BRDF, and the object class. Not all segments have a complete set of
  annotations; the experiments in this paper focus on the 58,928 that
  contain material names. Since material classes are highly unbalanced,
  only the materials that contain at least 400 examples are considered.
  This result in 53,915 annotated material segments in 10,422 images
  spanning 23 different classes.   Images are split evenly into
  training, validation, and test subsets with 3,474 images each. Segment
  sizes are highly variable, with half of them being relatively small,
  with an area smaller than 64 × 64 pixels. While the lack of exhaustive
  annotations makes it impossible to define a complete background class,
  several less common materials (including for example segments that
  annotators could not assign to a material) are merged in an “other”
  class that acts as pseudo-background.

Are there other scenarios where this term is used? Also, why exactly is it called a background class?
 A: It sounds like they are classifying material types where the material in question does not necessarily fill the entire image. The preceding sentence from the same paper

More recent datasets such as FMD and DTD
  remove this limitation by building on images downloaded
  from the Internet, dubbed images “in the wild”. However,
  in these datasets texture always fill the field of view of the
  camera. In this paper we remove this limitation by experimenting
  for the first time with a large dataset of textures
  collected in the wild and in cluttered conditions.

My guess is therefore that they are literally talking about a class of materials that are in the background of what they want to classify, which is a common term in image based machine learning where for instance a picture of a dog on a road requires learning the target class, 'dog', but also includes a background class 'road'. Note that an image might include more than one background class such as 'road', 'car' and 'sky' [1].
They go on to mention that

Texture
  is traditionally described by orderless pooling of filter bank
  responses as, unlike in objects, the overall shape information
  is usually unimportant. However, small under-sampled
  textures may benefit if recognized in the context of an object

So for them recognizing the background or context class is important as some materials show up with some objects and possibly even on some backgrounds more often than others.
Background class also seems to be used as a term for the majority class which contrasts what you are trying to classify. The terminology makes sense particularly for binary classification of varied datasets, for instance finding pictures of birds in mixed pictures of animals. In that case you are classifying 'bird' vs. 'not-bird' and it makes sense to look at bird pictures as the signal and everything else as the background noise.
tl;dr: In the cited example it seems like they are actually talking about the literal background and otherwise background class can be used as a synonym for majority class.
[1] Petra Perner: Machine Learning and Data Mining in Pattern Recognition, pg. 237
