Definition of a motif (in musical term) according to Wikipedia:
In music, a motif or motive is a short musical idea,[1] a salient recurring figure, musical fragment or succession of notes that has some special importance in or is characteristic of a composition.
A motif in a composition so important, that its composer keep repeating that in that composition, or present them in his other compositions.
The composer (or probably some other composers) can cleverly reuse (and hide the motif somewhere). The reason of doing so is that they save time not to recreate a whole new compositions to have listeners like/listen to them.
An example is that the motif in Final Fantasy VIII Laguna Battle Theme is similar to Auron’s Theme-FFX OST.
Let’s Look around Another World…
In software development, there is a similar concept called “Don’t Reinvent the Wheel.” In that case, developers use existing (usually open source) tools/libraries to build some essential functionalities. That is to prevent them spending time recreating recurring functionalities, and let them focus on the main logic. Sometimes, other tools can emerge from there.
Although it looks out of topic..
In my perspective, both are essentially similar.
