From my own opinion i think model by nature only depict a likesome of reality not a true and complete representation. Therefore, using the word abstract shows that it is just an idea or better say estimation of what the reality might look like. Abstract by definition is a phenomenon which is difficult to hold on to nor that is concrete but gives an idea of what is expected on ground.
I'm not an economist but with my little knowledge of economics, model in economics is only an aggregate of disjointed facts aimed at having a replica of such facts as reality on ground. I think an example is economic model of using Y=C+I+G+(X-M). These indicators joined together and are mere abstracts.
I think the aim of abstract models is to explain human's decision. We add abstract elements and assumptions to the model until we can derive refutable implication using real world data.
There is an important difference here between theoretical and empirical work. In theory you abstract from arguments that seem less important for the argumentation. But when estimating a model abstraction may lead to omitted variable bias. Taking arguments into account more broadly then is important.
Joan Robinson famously said in 1962 that "A model which took account of all the variegation of reality would be of no more use than a map at the scale of one to one." So the answer to the question really depends on what you are trying to accomplish with the model if you come at it from this perspective. My problem with this view is that it suggests that there is a relationship between the map and the territory and all we have to do is figure out the right level of abstraction (Joan Robinson's scale notion). My view is most theoretical models are not abstractions of reality but are representations of an economic insight that might be useful in looking at the real world. In macro, one of the most useful things about models is that they make us write down accounting relationships, which in turn helps us to remember things that can easily be forgotten.
A Definition of Abstract ( adjective): Existing in thought or as an idea but not having a physical or concrete existence: abstract concepts such as love or beauty .
Perhaps it might be used as a verb : to Abstract (usually abstract something from) Extract or remove (something): applications to abstract more water from streams. e.g. A Business Model is a representation of the reality ( of a set of business activities) where the modelling exercise is to faithfully abstract the core activities into a model which is an abbreviated but accurate representation of the reality.