I’ve just learned a bit of the て-form and now know it’s used for the progressive tense but I’m curious about what the difference between:
私は食べ物を食べます。
and
私は食べ物を食べています。
is?
My assumption based on what I’ve gathered is that the second one is in the moment and implying “right this moment” as though you took a bite after saying it, but I’m not entirely sure the circumstance you’d say the first one unless you’d usually use the second one.
The first is more like a description of a single action, like する just means “do”, whereas the ている describes an ongoing action, so している meaning “doing”
This can also be used in the past, if that helps show the difference, so (using your sentence),
私は食べ物を食べました。 ー> I ate food
私は食べ物を食べていました。ー> I was eating food
Yeah! You usually say 食べています when you’re eating (or like 食べているところで）and I think you usually use 食べます when you’re about to eat, saying you will eat something, talking about foods you eat, etc. So saying 私は食べ物を食べます is like saying “I eat food” or “I will eat food”.
私はたいていやさいをたくさん食べます。 I usually eat a lot of vegetables.
私はやさいを食べています。 I’m eating vegetables.
勉強してからこのお菓子を食べます。I will eat these snacks after I study.
Does that help? 
One key difference with the English tenses is that the Japanese “present” isn’t actually just the present, it’s the non-past. You can use it for future actions.
So this sentence ピザを食べます。ぴざをたべます。
can mean you eat pizza habitually, or that you will eat pizza later.
In that situation 食べます can correspond either to “I am going to eat,” or “I (habitually) eat,” in English. All distinction will come from context. 食べています means “I am (currently) eating.”
That distinction should get you through most simple sentences. As you encounter more Japanese, you’ll come across less intuitive uses of -ている conjugations to describe long-term or habitual actions, or to request an ongoing action of any duration, but it’s best to just take those as they come.
(Ex. 待っててください, which in practice is “Please wait (more than a little bit),” but would literally shake out to be something like “Please be waiting.”)