There are very many opinions of the "meaning" of the letters used to represent PIE reconstructions. One approach treats them as algebraic abstractions, where e.g. bh represents some sound that corresponds to φ in Greek and f in some positions in Latin, and b in English: there is no claim as to phonetic value. The other approach is that these are approximate hypotheses regarding the most likely pronunciation, thus reconstructed m is probably pronounced [m], and so on. Within the latter approach, there can be competing theories, for example some people reconstruct [d] where other people reconstruct [t'], that is there are competing ideas of what the substance of the proto-phonemes are. The strength of the argument for particular phonetic reconstructions varies, so while n is fairly uncontroversial (the reflexes are [n]), gʷʰ depends on sophisticated argumentation, since no language actually directly attests [gʷʰ]. The so-called laryngeals are a particular mystery, since they are preserved in no living though do show up in Hittite (where we don't really know for sure how things were pronounced).
The reconstruction of phonetic values is based on overlapping analogies and estimations of phonetic likelihood. For example, gʷʰ (a voiced aspirate labialized velar) is justified by the fact that that sound behaves like other voiced aspirates (is voiced in Germanic and Armenian, not devoiced), and acts like the other labialized velars (kʷ, gʷ) which are better preserved.
In other words, the letters represent hypotheses as to pronunciations, though with a certain limit on ability to reconstruct exact phonetics. I don't think there is much hope for reconstructing a very exact phonetic value of r, in light of the very many phonetic kinds of rhotics that exist, and even is one of the laryngeals is "ħ", there are quite a number of phonetic types of ħ in the world's languages, so some questions are probably unresolvable.