While it is true that a raga is hard to explain without being simplistic or reductionist, one must begin somewhere, and I think simplistic is better than nothing.
Essentially, a raga is defined in terms of its ascending and descending scales (aroh and avaroh). For instance, if you have the Dorian mode (kafi scale in Indian music), you could use all seven notes in that scale, or you could use some of them. You could have the ascending and descending scales mirror each other, or not. In this way, you can get many different ragas from each scale. The video below shows how this works by demonstrating the aroh and avaroh of several ragas derived from the Dorian and natural minor scales.
How a raga is different from a scale - One scale, many ragas
Because of the structure of ascending and descending scales, and a few other factors, certain natural pathways open up for the melody of a raga to flow in. For instance, if a raga skips Re (the second note) in the ascending scale, but uses it in the descending scale, then ascending phrases will always skip that note, while descending phrases can use it.
This flow of a raga's melody is called "chalan," and Indian musicians will often discuss ragas in terms of their chalan. The video below demonstrates how two ragas, Raag Bhimpalasi and Raag Bageshree, while using the exact same set of notes in total, sound very different because of their different chalans.
"Chalan" - The flow of a raga's melody
Apart from the aroh and avaroh and chalan, there are several other elements that define a raga. These include ornamentation typical of each raga, vadi and samvadi notes, which are focal notes around which a raga revolves, nyasa notes, which are notes on which phrases in a raga end satisfyingly, deergha and alpa notes, which are strong or weak notes in that raga. The video below demonstrates how Raag Bhimpalasi and Raag Dhani, which are fundamentally very similar, still have unique identities because of differences in how their notes behave.
The defining elements of a raga - aroh, avaroh, ornamentation, vadi, samvadi, nyasa, deergha, and alpa notes
If you'd like to read more about the different kinds of ragas (symmetric, asymmetric, mixed, compound, and circuitous ragas), you can do so here:
Different kinds of ragas by structure
Source: Please note that all the information and link to the page on different kinds of ragas by structure are from my website on Indian classical music, which I run as a free educational resource. The Youtube videos are from the Youtube channel (Raag Hindustani) affiliated with the website.