Summary: Martha has to believe that the Doctor can save the earth.
Martha thinks that to anyone but the Doctor, the situation on earth would appear hopeless. The Master is in control, destroying cities and people on a casual whim. His emissaries, the Toclafane, carry out his orders gleefully; they seem to delight in murder as much as the insane Time Lord himself.
Even though she doesn’t fully understand the Doctor’s plan, Martha does her part willingly. Walking the earth, spreading the word, is exhausting, terrifying, and lonely, but she clings to hope because it’s all she has.
As long as the Doctor lives, there’s no such thing as a lost cause.