A term from Sanskrit phonetics, used in English. In the Devanagari script it is two dots one above the other at the end of a word, and indicates the sound h. In romanization this is indicated by an h with a dot under it; on the Web we write either h. or (in The Harvard-Kyoto system of Transliteration) H, to distinguish it from the letter h written elsewhere in a word, which has a different origin.
It is a voiceless fricative, that is a whispered h the way it usually is in English. As this is difficult to pronounce finally, a light echoing vowel is often added after it to make it clearer, so as'vaH may be said as'vaHa. This also distinguishes it from the other h, which is voiced and derives from other voiced sounds in Proto-Indo-European, the ancestor of Sanskrit.
The visarga has two origins, s and r. Compare Latin equus and quattuor, the words for 'horse' and 'four', and Greek hippos 'horse': in Sanskrit these are as'vaH and catuH. The former is from the very common Proto-Indo-European masculine nominative singular ending *-os.
In sandhi, the change of consonants depending on what sound follows, the visarga may become either s or r depending on complicated rules.
It usually occurs only word-finally, but may be found at the end of internal syllables too, e.g. duHkhaM 'unhappiness'.
The visarga only occurs in the classical language Sanskrit; it disappeared from its descendants the Prakrits and modern Indic languages. Words and names taken into English usually leave it out too, because the visarga and the anusvara (neuter -M ending) are just case endings on the stem, which ends in a, e.g. candraguptaH = Chandragupta and yogaH.