At the opening of Sophocles' tragedy Oedipus the King, the city of Thebes is in the midst of a terrible plague. After the Theban king Oedipus promises that he will do everything he can to help remedy the situation, a priest of Zeus addresses Oedipus and gives further details about the plague and the plight of the Theban people. He recalls how Oedipus has been haled as the savior of the city, an allusion to Oedipus' solving the riddle of the Sphinx, a monster that had killed a number of Thebans.
Thus, the priest's comment "that we first stood straight" alludes to Oedipus' saving the Thebans from the Sphinx. This may also allude to the riddle of the Sphinx: "What walks on four feet, then two feet, then three feet..." The priest's remark about standing straight may hint at the part of the riddle about walking on two feet. Oedipus' solving of the riddle allowed the people of Thebes to walk on two feet, to walk upright, for the first time in a long time.
There is also irony in the fact that Oedipus himself has difficulty in walking due to his feet being pinned together when he was an infant. The name Oedipus can mean something like "swollen foot." So, it is ironic that Oedipus allowed the city of Thebes to stand upright although he himself cannot stand perfectly upright.
The priest's comment is also ironic in that it foreshadows the situation that will exist at the end of the play: by the end of the play the people of Thebes will recall of Oedipus' reign that he "first stood straight, but stumbled later."