As with many topics, especially in the world of guitar effects, "buffer" can be a controversial term. Sometimes you'll hear you must have one, or you mustn't, or you need a certain one, or that it's "just a buffer" so it doesn't matter which one you choose. I'd like to present my views on the subject, as well as try to move past the jargon and clickbait-titles.
You'll notice I put the term "buffer" in quotes. This is because, from a certain perspective, buffering is something a circuit does rather than is. Buffering can be viewed as the process of isolated, active impedance conversion, meaning receiving a high-impedance signal and transmitting a corresponding lower impedance signal. This is a very important task, and many circuits can be said to accomplish this. Some of them do only this, while others may add gain or distortion or perform other tasks.
A very brief history of impedance in audio circuits may be in order - In the early days, and in some cases to this day, impedance matching was/is the preferred method. This would mean that the output impedance of one device would match the input impedance of the next, and all would be good. But in a world of lots of different devices made by lots of different people for lots of different reasons, these impedances wouldn't match and there would be problems. I will leave the detailed description of what problems and why to another brave soul, I don't feel I can do that topic justice. But suffice to say, impedance bridging became the preferred method over time, meaning that as long as the output impedance was sufficiently low and the input impedance sufficiently high, few problems would be had and different bits of gear could mix more happily. This is how most guitar pedals work, relatively low output impedance and relatively high input impedance. Notice there is no specific number given. This does not mean that input impedance should be as high as possible in all cases, or output impedance as low as possible, because that would have it's own set of problems. No, just that in a given system relatively low output impedance matched with relatively high input impedance will yield the best results in most cases. If a person were to claim something like, "input impedance should be 1 megOhms and output impedance should be 100 Ohms," that person would be wrong. In fact, a few good-sounding classic pedals have input impedances as low as 100K. The only stage that is helped by being 1 megOhms or higher is the first stage seen by the passive output of the guitar - but even that has caveats.
Now, there are very simple devices that will do this job. When you hear someone say "just a buffer," they probably mean a source follower or a voltage follower. A source follower is a discrete device, the simplest form of which uses a single FET. It's also called a common-drain amplifier. Simple class-A buffers are often this circuit, but you'll also see common emitter FET amplifiers wired up to make little or no gain and referred to as a buffer. The opamp version of this is called a voltage follower, and it's also extremely simple. These devices do the job of buffering, both alone and inside larger circuits, and their strengths are largely their simplicity and affordability. You can make these circuits with very few components, and they draw very little power. They may not have the highest headroom, or best phase response, or best transient response, or output drive capability, but in practice they can often work just fine.
This is where we diverge from facts into more murky waters. What makes a circuit "good-sounding" is entirely subjective, and circumstantial, and it's not my goal to disparage any circuit, pedal or person who might choose that simple solution. We all walk our own path. The Tillman boost, which is very similar to the much-loved input preamp of the Echoplex, is an extremely simple circuit that everyone knows sounds great. Simple voltage followers like the buffer in a Klon Centaur can also sound pretty good. Why then would a person like me build a more complicated device? Well, I genuinely think the sound of those simple devices leaves something to be desired in most circumstances. With a more complicated device, and with more expensive components than would be feasible in a simple low-cost circuit, it's possible to achieve what I consider to be a higher fidelity sound, more reminiscent of the guitar-plugged-right-in sound. There are some simple tweaks and some complicated aspects, but suffice to say both the R&D time and the component cost are significantly higher than with a simple voltage follower circuit.
When you get to the audiophile terms, there's no way around the comical language. To say a circuit has "snap," or "feels better under your fingers" is really hard to quantify, and I'm extremely thankful that a lot of players have confirmed that EUNA does this or I might feel like I was going overboard a little bit. "Chime," "sparkle," "new string feeling," this is how it's described, sometimes by me and sometimes by 3rd parties. I definitely see the humor in it, believe me, but metaphorical language sometimes has to pick up when technical language fails to describe the feel of a musical amplifier circuit.
If you have any pedals at all between the guitar and the amp, something is buffering. It may not be a device that is particularly suited to the job, but if there's an active device down there on the floor it's buffering whether it likes it or not. One of the reasons I designed an overbuilt device like EUNA was this knowledge - something is buffering down there, so I want it to be good at the job and dedicated to it. Could I have used "just a buffer?" Absolutely. But knowing how critical the first amplifier stage is to the passive output of the guitar, I wasn't satisfied with the performance of those simple devices. Again, that's not to say that being satisfied with that device would be bad, or wrong, or that they are poor devices. They do exactly what they were designed to do, they are "just a buffer." In designing and building a dedicated, ground-up design I've satisfied my own criteria for a bullet-proof, better-sounding input driver that replaces a conventional buffer.
So, when someone says something is "just a buffer," the kindest thing they could mean is that the device is a source follower (also called common drain) circuit, a common emitter amplifier circuit wired for no gain, or a simple opamp voltage follower. These devices are sufficient for many players, and are also great first builds if you are getting into DIY pedal building. EUNA is a two-stage amplifier circuit that is set at unity gain, with a massive internal power supply, so that it can perform the function of buffering your signal to a higher degree of fidelity and musicality than a conventional circuit. Very much not "just a buffer."