In short, Teiresias believes fate is an unstoppable force and acts as a foil to Oedipus, Laius, and Jocasta, who try changing destiny. For Teiresias, humans cannot change fate and therefore have no real free will.
Though Teiresias can see the future, he feels that trying to alter the events he witnesses in advance does no good and that everything that happens is the will of the gods. Even if one tries to fight fate, as Oedipus and Jocasta try to do, the effort is futile. For this reason, Teiresias initially refuses to share his visions with Oedipus: not because he is unpatriotic as Oedipus initially accuses him of being, but because he feels that to share would be pointless anyway ("Well, it will come what will, though I be mute"), bringing Oedipus only more pain before his tragic fall comes as it inevitably must. He only shares his visions once Oedipus goads him into doing so.
Teiresias's attitude towards his gift of prophecy is one of absolute confidence, further reflecting his unshakable position on fate's power over free will while also providing an unspoken irony: if humans cannot change fate, then prophecy might be rather useless. Even so, Teiresias believes in accepting fate rather than struggling against it. Even when Oedipus accuses the prophet of being "offspring of endless night" with no power over either him or people who can physically see, Teiresias parries that unlike Oedipus or those more physically able-bodied, he "leave[s] to Apollo what concerns the god." That is, he accepts that the gods have more power than he and does not try to fight destiny, an act which proves to be the downfall of Oedipus and Jocasta.