Ask HN: please help me understand latest trends in database design

I'm naturally a front-end guy but database design and back-end dev has piqued my interest the last few days and I'm lingering very confused. I'd like to fully grasp these concepts so my head doesn't hurt anymore.

I'm used to dealing with an ORM like active record. When I imagine my user objects through rails I picture an object of a person being related to a row in the people table. Ok basic.

So, I read that non-relational databases like mongodb aren't just cool because they're "fast with big data" but they're also cool because they apparently make developing more natural with an oop language (why?). Then I also read that most design patterns probably aren't truly relational. Ok, this is where I get lost.

1) What are some fundamental examples of relational design and non-relational design? 2) similar to above, what are examples of structured data vs unstructured (is this just rephrasing above?)

So, given those things I feel (in my immediate ignorance) that almost every type of project I've attempted to model against has been relational. But maybe I'm just using semantics over technicality. For example, posts and comments. Relational to each other. Add users in there. it seems most apps these days have data that is always useful to reach through other data/objects. That's relational isn't it?

How about something describing something less typical.

Let's say I was building a workout tracker app. I have users, exercises, workouts, routines and log_entries.

I create a routine to group workouts. A workout is a group of exercises. I record my reps and weight through log entries for my exercises. Is this relational data or non relational? Would mongo be great for modeling this or awful?

I hear things like statistics come into play. How does that affect the above example? What statistics are people usually speaking of?

Let's say I added tracking other things, like a users weight, height, body fat and so on. How does that affect things?

Thank you for taking the time to help me understand.

Edit: can anyone explain why it may be easier to develop for one over the other. Is using something like mongo more agile both because it "clicks" more once you "ge it" and also because you don't need to run migrations?

Another thing, when using an abstraction like an ORM - does it really matter? If so when? To me the initial value would be the ease of querying data and modeling my objects. Whatever lets me do that easier is what I'd be happy with. I truthfully do find myself scratching my head a lot when trying to model data.