linguistic distance canbe an impeding factor in SLA WHEREAS linguistic proximity can influence linguistic fluency of learners. .according to a plethora of studies, Language Distance is thought to be one factor affecting the ease or difficulty with which learners acquire target language. it can influence syntactic structures, semantic and phonetic aspects of learning. best
This is a very broad question that deserves a really long answer, but very generally linguistic distance can either be defined in terms of phylogenetic distance / (un)relatedness or in terms of typological distance independent of phylogenetic distance. Whereas the former concerns how closely related a set of languages are, the latter involves similarities and differences in terms of typological traits, e.g. phonological, lexical, morphological and syntactic (dis)-similarities. These tro often go hand in hand but do not have to, due to e.g. contact effects between unrelated (but geographically closely) languages or by pure chance.
One of Gerhard Doerfer's articles is on Mongol-Turkic languages kinship. He compared the two languages in terms of basic vocabulary. According to Doerfer, to claim kinship between two languages can only be possible If they share at least 50 words of basic vocabulary. https://books.google.pl/books/about/Temel_s%C3%B6zc%C3%BCkler_ve_altay_dilleri_sorun.html?id=B1P-oAEACAAJ&redir_esc=y