Garden asparagus (Asparagus officinalis, asparagus family, Asparagaceae) has been cultivated since Roman times (see last week's post link), so there is interesting folklore.
It was and is considered an aphrodisiac. It comes up as phallic shoots in the spring. Historically and prehistorically people celebrated spring as a rebirth and time of renewed reproduction. Asparagus shoots fit well into that. Cultures from Greece to England have included asparagus in spring (fertility/Easter) festivals, both as food and in decorations from bouquets or chaplets (little wreaths worn on the head).
Apart from symbolism, asparagus shoots are one of the earliest vegetables of spring. If you imagine Europeans living all winter on dried peas and pickled cabbage, having fresh vegetables would not only be a delight, it would provide nutrients that were likely missing in the winter diet, so indeed fresh asparagus would act as an aphrodisiac.