Gilly Brownlock was a Shire-hobbit who joined the Baggins family when she married Posco Baggins, son of Polo. Through their three children Ponto, Porto and Peony, Gilly and Posco gave rise to a populous branch of the family, though none of their descendants played an important part in the War of the Ring. Gilly's husband Posco seems not to have survived to see Bilbo's famous Bilbo's Farewell Party, but Gilly herself (who would have been roughly a hundred years old at the time) was among those who saw Bilbo Baggins disappear.
Gilly is perhaps a reference to gillyflower; aka wallflowers; or Dianthi with clove-scented flowers. The name derives from French gilotre, from Greek καρυόφυλλο "clove tree"