You won't find a definite, unambigious answer. Here's my stab at it.
Context: in the third prologue, Zarathustra is teaching the people about the Übermesch. A human is somewhere between a monkey and the Übermensch. The human is something to be overcome, Z. teaches the goal of Übermensch.
Let's break down the quote:
Z. says 'even the wisest'. Wise people are sometimes referred to as philosophers.
The most open to interpretation is 'plant and ghost'. It may be reference to Aristotle's teaching of the soul: the vegitative soul, the animal soul and the mental soul. Plant refers to the vegetative soul, ghost to the mental soul. And worm and monkey from earlier in the speech to the animal soul, but plant and animal are drawn together in my interpretation here.
Philosophers have fixed their interpretation of the human as a combination (mix) of the vegetative/animal, and the mental. Formerly this is called: the human is a zoon logon echon in Greek, animal rationale in Latin and rational living being in English.
And as a conflict between them, remember Plato's famous Chariot allegory: the mind controls the two horses of passions. In philosophy, an opposition between the body/passions (plant) and the mind (ghost) is common.
Somewhat further, one can extend this conflict of plant and ghost as reference to the conflict between matter and mind, between body and spirit, between realism and idealism, between empiricism and rationalism.
Nietzsche/Zarathusta, however, does not want humans to be plants or ghosts, to be hedonists or rationalists. Why? Because in that way humans remain fixed as a rational animal.
In other words, the human as a rational animal is a current or old value. If a philosopher preaches you to indulge in your desires (i.e. be a plant) or on the contrary to be rational (i.e. be a ghost), he accepts the characterization of humans as rational animals.
Z. preaches the reevaluation of all values, including this one. Humans (or, perhaps better, this fixation of human beings as rational animals) should be overcome. Human as conflict of plant and ghost, of matter and spirit, should not be merely assumed and taken as a starting point for a debate where one chooses one side or the other. Rather this value itself should be questioned, and perhaps thereby be overcome. To a new self-understanding of the human being.