Well, whenever I describe the word "engineering" the first thing that comes to mind is "problem solving."
Suppose you work for an engineering firm, you can be contracted with a certain problem (anything from a brand new design to a process optimisation). You would then research / review prior art, brainstorm possible solutions, run a cost-benefit analysis and compare the merits of each possible solution you come up with (often there are a lot of them).
Ultimately what that boils down to is you've selected what you and your team think is the best possible solution. After that you start entering the design phase, and eventually you'll be able to construct a prototype to report on.
My university handles first year engineering as a more general field before branching out in to majors. All first year students have to partake in one of four different projects each for semester 1 and semester 2, and ultimately a prototype (working or not) has to be constructed by the end of semester.
My first project was an environmental engineering project with Engineers Without Borders, which was the design of a sanitary latrine / toilet for developing countries for which any waste would be safely reusable as fertiliser with no risk of disease. My second project was an automated mixer which would be able to mix two streams (hot and cold) and achieve an overall desired output temperature, and that was able to deliver 10L within 5 minutes. Both sound simple, but there was a lot of work for people who had never done it before and it was very fun.
My major is currently chemical / process engineering. It's particularly useful in pharmacy, bio-engineering, nanotechnology, mining, refining, environmental sustainability, and so on. I was actually involved in a project at the Australian Institute for Bioengineering and Nanotech. briefly in regards to a biodegradable plastic produced from bacteria, which was quite fascinating.
Well I hope to get accepted to do an electrical engineering course focusing on wind powered renewable energy this autumn

I suppose you would recommend engineering if I were to ask?
I'm quite interested in the design and building side myself, but depending on how you specialise it obviously branches in to different fields but what I suppose the average person would describe it as is machines, maintenance and getting really greasy
The grease monkeys are the mechanical engineers, haha. Electrical engineering I think you'll find is both fascinating, difficult, and involves a lot of sitting in a lab wondering why your circuit doesn't work (oh the painful memories). Certainly, I'd recommend engineering though, as you can probably tell by what I just wrote that it's incredibly diverse and fulfilling.