Because sometimes it just sounds better to use one word instead of "an hour and a half." This is one of a family of words using the Latin prefix sesqui-, meaning one-and-a-half of whatever units the root refer to. Cousins include sequipedalian "a foot and a half long," sesquicentennial "a hundred-fiftieth anniversary," and sesquidecury "a set of fifteen." Not coined from Latin roots but rather adopted from Latin sesquihora, the period of an hour and a half. (BTW, I've stopped saying that a word is "borrowed" from another language -- it's not like it can be given back.)
I ended up taking a sesquihoral lunch.