Pale, round pods of a ginger-family plant, full of small dark brown seeds with a cool, eucalyptus-like scent. A few go into the spice mixes for braised meat; 肉豆蔻, nutmeg, is a different spice.
The figurative meaning comes from Tang poet 杜牧 (Du Mu)'s line 娉娉袅袅十三余,豆蔻梢头二月初 - comparing a graceful 13-year-old girl to a cardamom bud in early spring. Hence 豆蔻年华 'cardamom-bud years' = a girl's early teens.