What term/theory describes more efficient utilization of a resource? I may be asking the wrong question here, but I wonder if there is a term/theory that describes/studies the evolution of an economy that continually improves the utilization and allocation of certain resource? The resource here can be different things, e.g. physical goods, human labor, financial capital. In fact, I am more interested in the former two than the latter.

For example, living space used to be mostly utilized by the its owner or long-term occupier, and many were under-utilized in terms of both the utility of having people living in them and the monetary value extracted from them. Now some significant portion of these spaces is better utilized by services like Airbnb. A similar case is car-sharing services like Uber and Lyft, where both cars and human labor are arguably better utilized and allocated.

To clarify, I am not specifically interested in the so-called 'share economy' concept though the two examples above are closely related to it. Actually it'd be better if you can identify other examples in different contexts. Pointers to any related term/concept/theory is welcome and appreciated.
At the abstract level, this phenomenon is covered by the concept of "Technological Change", which, in Economics, does not have a strict/narrow "Engineering" interpretation: here, "Technology" is not only "how things are done" but also "how things are organized", and includes also new business models like the one you mentioned (see also this post).  

So the phenomenon is already embedded in the logic of economic models.  

Stochastic Frontier Analysis (SFA) and Data Envelopment Analysis (DEA), are two sub-fields focusing on modeling and measuring the degree of efficiency (under various interpretations of the term), in the use of factors of production at the micro-level.  

It is my impression though that since the examples you describe are relatively new, we still do not have enough data available to subject them to econometric analysis, so I cannot say if there are already papers that examine them (in a quantitative way).