Wiktionary
aspirated h
n. (context linguistics English) In the French language, usage of the letter h at the start of a word which does not allow liaison with a preceding consonant or elision of a preceding schwa.
Wikipedia
Aspirated h
In French spelling, aspirated "h" ( French: "h" aspiré) is an initial silent letter that represents a hiatus at a word boundary, between the word's first vowel and the preceding word's last vowel. At the same time, the aspirated h stops the normal processes of contraction and liaison from occurring.
The name of the now-silent h refers not to aspiration but to its former pronunciation as the voiceless glottal fricative [h] in Old French and in Middle French.