Google says "characterized by comprehension of the parts of something as intimately interconnected and explicable only by reference to the whole", and I'm more confused than anything.
One "holistic" approach (in my mind) is a broad accounting of stocks and flows. For instance to evaluate the possibility of building a space sunshade with a solar sail factory on a carbonaceous chondrite asteroid it would be reductionistic to design the system and mission in as much detail as possible, It is another to say that you need to make 10^14 kg of mylar and 10^12 kig of aluminum and make some broad guesses about stocks and flows from there. That's more holistic.
I would say use of the holographic principle in quantum gravity is holistic, adding up thousands of Feynmann diagrams is reductionistic.
The original meaning was about wholeness: studying or managing something as a whole.
It has been co-opted by alternative medicine, which is where you'll see the word most often. There is (and should be) a concept of holistic medicine, which could mean seeing the body as a whole instead of individual systems. Real medicine is going in this direction anyway, for example with the growing understanding of the link between the brain and gut.
For people marketing alternative medicine, it's a buzzword that makes people think of wholesome, and also that the seller is considering things that science-based medicine is missing.
For example, if you review a car, like in the publication Car and Driver, you might look at the engine and rate it, but it would be within the context of that car. You could have a high output engine and weak brakes, which might make the car less attractive from a holistic view (and maybe dangerous). You want to see how all the parts of that car 'add up' as a complete system.
It literally means looking at the whole picture -- "whole-istic" would be a misspelling, but makes the meaning more clear. See all parts of a system as a pieces of a bigger entity, and recognize that what impacts one part will impact the whole.