First, this is a specialist term. Much like vocabulary in medicine, engineering, math and sciences, software development, etc. The same term may be used across these domains with radically different meaning. As such it must be noted while this most certainly is an important term in the IT domain, use outside of this domain is probably a mistake.
Solutioning is a commonplace term in IT and IT recruitment. In IT there is the common job title solution architect. A solution architect is someone who provides IT solutions in a particular domain, often software development but there are solution architects in Data Warehouse(DW), Storage, and many other IT domains.
I would define it as the process of creating solutions. The distinction that should be noted is that many issues arise. All programming in a sense is problem solving, but regardless of the specific type of solution architect their ongoing duty is to solve problems. They are not hired to solve specific problems (although certainly quite a number of such would be identified) but also solve future issues. For this reason they describe their work as "solutioning", a term which encapsulates this idea of an ongoing problem solving process.
A further part of the etymology, is the link in software development from mathematics. That is, in software development a piece of software is often refereed to as a "solution"(among developers anyways). Like functions in math, software takes inputs and returns outputs. At the small level this occurs in software functions, at the larger levels in more abstract ways. But the point to take away is that during development you're plugging these systems together, each part complete in it's own right. Each sub-component a "solution" to some part of the problem. The work is software development and solutioning is highly related term, but when we think of the former we think of programming while the later refers to a concern at a higher level. This is why we say the architect performs solutioning, and it is an activity that is nearly exclusive to the domain of IT architecture (at least at the time of writing).