Identity by descent among unrelated individuals
The definition of IBD is always the same - an allele or segment of alleles which is shared between two individuals because of descent from a common ancstor.
In the context of this paper, the authors are referring to segments of the genome between individuals which are IBD. In this case, they are looking at recently isolated populations who are likely to share longer stretches of IBD with one another. This is the case because each individual within a relatively isolated population is likely to be, on avergae, more related to another individual than in an outbred population. In general, it it much easier to detect longer segments of IBD than shorter segments, and this is why they choose to study isolated populations. Also, you can be much more sure that longer IBD segments will share a common ancestor with one another.
More specifically, they define a 'large' IBD segment is one which is longer than L centimorgans of length. Additionally, they define 'IBD-sharing' level between two individuals, as the probability that a randomly chosen genomic position on homologous chromosomes from each of the individuals lies in a large IBD segment shared by the two individuals. Thus IBD sharing takes values between 0 and 1.
There are several different methods, such as PLINK, fastIBD and GERMLINE which can identify IBD segments and their corresponding lengths from genotype data.
If you are interested in a relatively accessible guide to understand the principles of both single locus and segmented IBD, then I would recommended checking out Graham Coops's population genetics notes, section 2.2.