Q:

What makes a DNA sequence motif a DNA sequence motif?

I've read about DNA sequence motifs, but still don't understand what makes some sequence a DNA sequence motif. Is this a well-defined concept? For, example, 
What are DNA sequence motifs? says:

Sequence motifs are short, recurring patterns in DNA that are presumed
  to have a biological function. Often they indicate sequence-specific
  binding sites for proteins such as nucleases and transcription factors
  (TF). Others are involved in important processes at the RNA level,
  including ribosome binding, mRNA processing (splicing, editing,
  polyadenylation) and transcription termination.

For example, I've been working with Recombination Signal Sequences (RSS), which are important in immunology. However, from what I can tell, RSS are not themselves motifs, but they do contain motifs. E.g. Conservation of sequence in recombination signal sequence spacers
says

Previously, the RSS has been described as possessing both a conserved heptamer and a conserved nonamer motif.

So, apparently, the heptamer and nonamer component of the RSS are themselves motifs, but the RSS itself is not. Can anyone explain why? Thanks.

A:

Motif means a pattern. For any array of objects to be called a pattern, it has to have at least more than one instance. 
To define more precisely, a motif should have significantly (statistical) higher occurrence in a given array compared to what you would obtain in a randomized array of same components (expecting at random). 
[Here i use the term array to mean an arranged set such as a genome (array of nucleotides with their position in the sequence) or a protein structure (array of amino acids with their vector positions). A randomized array with same components is generated by shuffling the elements and their values; for e.g. assign the same collection of nucleotides to random positions] 
RSS nonamers/heptamers are called a motif because they are a pattern of sequence which a) has more than one occurrence b) the occurrence is significantly higher than a random expectation. Generally in sequence motifs randomization is not usually done because the genome size is too huge. In such conditions if your sequence has >= 2 occurrences throughout the genome it may be considered a motif. Lets assume a 10bp sequence. Its random probability = 1/4¹⁰. Therefore in 1048576 bp (1Gb) there is a likelihood of finding one instance of that sequence on random. So I assumed that if that sequence has >=2 instances it can be called a motif. However, I am not sure about this.
RSS is not a motif because the entire RSS is not conserved; the conserved 'motifs' are interrupted by sequences. This is analogous to lets say a promoter which is a functional region of the DNA. Promoter can have binding sites for different transcription factors and these operator sites (TFBS) can constitute a motif (if they are conserved) but not the entire promoter.

