The numbers are specific to Proto-Indo-European.
Scholars aren't sure how PIE was pronounced: after all, there are no native speakers around now, or records from the time. All of the sounds in reconstructed words are educated guesses at best.
Some sounds were fairly easy to guess. For instance, there was a sound that seems to have become
/t/ in most of PIE's descendants. Thus, it makes sense to call that sound *t.
But others are harder to guess. The well-known linguist Ferdinand de Saussure argued that PIE needed a few extra sounds to explain all the evidence, sounds that didn't have direct reflexes in any Indo-European language known at the time. (Since then we've found one family of languages which has reflexes for these sounds, which adds evidence to his theory.) He simply called these unknown sounds "coefficients sonantiques" and didn't speculate as to what they might have been.
Since they were probably fricatives, and weak fricatives at that, people took to writing them all as *h. Except that there were three different ones. So with typical lack of creativity, they're now written *h₁, *h₂, and *h₃. There are various theories as to what they actually were, but the notation has become standard now and is unlikely to change. Personally, I'm fond of Rasmussen's claim that *h₁ was a glottal fricative (English "h"), *h₂ was a velar fricative, and *h₃ was a voiced velar fricative with lip rounding. But many other linguists would disagree. Some say *h₁ was a glottal stop, others say *h₂ was uvular, and so on.
In Semitic reconstruction, by the way, there was a similar problem: Semitic languages tend to have multiple sounds that are sort of like
/h/, and it's not clear what the original forms were. So they're conventionally transliterated *h, *ḥ, *ẖ, *ḫ. The moral of the story is we really need better conventions for writing "h-like sounds".
As far as the superscript w, that's standard linguistic notation for lip rounding ("secondary labial articulation"). PIE distinguished between velar consonants and rounded velar (aka labiovelar) consonants, roughly equivalent to the difference between English "keen" and "queen". Some transcriptions use a normal *w instead of the superscript, or even a *u; it's just a matter of style. (No matter which style is used, though, the rounded consonants are generally considered single phonemes, not clusters of a velar and a labial.)