To begin to approach quantum mechanics, you have to accept that on that very tiny scale, the world does not behave in a way that's intuitive to human experience. Everything you see and interact with as a human is in truth just some macro-scale approximation of an incomprehensibly number of complex relationships formed at unthinkably small scales. So with your human intuition set aside, you're ready to wade into QM.

For purposes of your question, it's probably best to start with the double slit experiment, which hails from the 19th century. I'll trim the fat to keep the ELI5 short, but definitely google videos about this experiment to gain a deeper grasp of what it shows and why that's important. But essentially, the double slit experiment shows that photons (light particles) can behave both as particles and as waves. Photons seem to act particle-like when you squeeze them through a narrow slit, but on the other side, it starts to interfere with itself in a wave-like fashion. This was puzzling, and took us a while to figure out.

In the 1920's, the Heisenberg and Schrodinger you've probably heard about got together and kind of cracked the code behind this strange quantum behavior. Heisenberg pieced together that there is an inherent uncertainty when you try to measure a particle's momentum and position. You can get an arbitrarily highly precise measurement on one of them, at a proportional sacrifice to precision on the other. This is the Uncertainty Principal. At the same time, Schrodinger developed his famous equations, which described quantum systems not in terms of discrete particles, but as single "wave functions." A wave function is sort of a probabilistic expression that describes all of the potential states a quantum system, accounting for this uncertainty. The wave function is a sort of sum of all these potential states, weighted by their probability. In that way, the wave function comes to approximate (very, very precisely) the "superposition" behavior of quantum systems, wherein the system behaves like a mix of all potential states it could take. Schrodinger's equations described how such systems evolve in this probabilistic fashion, and experimentation has justified him time and again.

Now, to return to your question, physics is much less concerned with answering "what things are" at a fundamental level and much more interested in answering "what things do." So we can only really answer the first question in terms of the second. To that end, we see that, at a fundamental level, the universe does not behave classically, but instead its constituent particles behave according to the everywhere-at-once oddity of QM. So we can say that fundamental particles are not simple points of mass or energy--they behave according to a much deeper and more vibrant structure.