What sort of elixir does Mrs. Joe give pip? Why?

The elixir is called tar water and it was pretty vile stuff,

"Some medical beast had revived tar-water in those days as a fine medicine, and Mrs. Joe always kept a supply of it in the cupboard; having a belief in its virtues correspondent to its nastiness. At the best of times, so much of this elixir was administered to me as a choice restorative, that I was conscious of going about, smelling like a new fence."

Tar water was "a Medieval medicine consisting of pine tar and water".