Here are my thoughts on what an "engine" is.
Slogs aim to draw the game out and play few actions per turn. rushes aim to get the cards they need quick and then pile out. Big Money (BM) buys few actions, mostly money, and aims for provinces, then duchies.
Combos and Engines are what remain. Combos are basically each in their own category, so we'll ignore them. (A learning player like yourself needn't concern yourself with these relatively exotic decks, but if you enjoy just reading about the game, you can look up chancellor/stash, hermit/market square (especially challenging to pull off), native village/bridge, native village/apothecary, to see what I'm talking about.)
Basically, an engine is a deck where you play a lot of actions that work together to become more than the sum of the parts.
A draw-to-X engine (library or watchtower) is a good example of how deck synergy works. Festival is good but lacks draw. Library is good, but playing several in a row doesn't help you. However, if you can play lots of festivals (and/or other cards that produce $$ and reduce hand size, e.g. bridge, oasis) in between libraries, then the library draws a crap ton. When you play a lot of actions that synergize, that's an engine. (Drawing your deck is kind of a side-effect in my view.)
I guess a village and smithy don't really "synergize" particularly by themselves, but then by themselves they make for an "engine" that will consistently lose. You need other cards (generally some combination of attacks, trashing, +buy, and alt-vp) that make the village/smithy interaction worth setting up, and that's synergy.
A beginning player like yourself can learn a lot by mastering the basics of big money. Once you get a feel for the strength of big money (that is, when you look at a board, you should have a feel for how strong BM will be on that board), you can begin to get a sense of where engines are worth building. Note that really weak Big Money support is another reason to go engine.