What a tone generator is actually good for
Four things, and it is worth being precise because it is also commonly misused.
Tuning by ear. A4 at 440 Hz is the international reference, and every other note follows from it. Playing a reference tone and matching an instrument to it works perfectly well without any app.
Checking that audio output works at all, and which channel it comes out of. A sustained tone makes a dead speaker, a loose cable or a wrong output device obvious in a way that music does not.
Finding a resonance. Sweeping slowly through the low end will find the frequency where something in the room rattles or a cabinet buzzes, which is how you locate a problem rather than guessing at it.
Masking. A low steady tone can cover an intermittent noise, though pink noise is usually more comfortable for that.
Start quiet, and here is why
A pure tone is deceptively dangerous. Music spreads its energy across the whole spectrum, so a given loudness is shared out. A sine wave puts every bit of its energy at one frequency, concentrated on one small part of your hearing.
Two consequences. It is more damaging than music at the same measured level, particularly above about 4 kHz, and the damage is cumulative and permanent. And it sounds quieter than it is, especially at high frequency, so the natural instinct is to turn it up.
Tweeters are at risk too. A continuous high-frequency tone at volume delivers sustained power to a driver designed for brief transients, and they do fail this way.
So set the volume low, then raise it if you need to. Never start a high frequency at a volume you have not tested at a low one.
Choosing a waveform on a frequency generator
Sine for anything that counts as a measurement. It is a single frequency with no harmonics, so what you hear is exactly what the number says.
Square and sawtooth add a strong harmonic series, which makes them sound bright and buzzy and much louder at the same amplitude. They are useful for hearing whether a system distorts, and they are the wrong tool for testing a specific frequency because they contain many.
Triangle sits between: fewer harmonics than square, softer and slightly hollow.
Note names and equal temperament
The tool shows the nearest note to your chosen frequency along with how far off it is. The mapping comes from equal temperament, where each semitone is the twelfth root of two times the one below it, anchored at A4 = 440 Hz.
That is why the note frequencies are mostly not round numbers. Middle C is 261.63 Hz, not 262 or 260. The presets give you the exact values.
Everything is generated in this tab by a Web Audio oscillator. Nothing is downloaded, recorded or uploaded.