I assume you are refering to the first speech from the Chorus in this play, which is a kind of victory chant for the success of Thebes against the invading army of Argos. The army of Argos is described as being like an eagle in this speech. Note how the Chorus develops this comparison:
And he had driven against our borders,
launched by the warring claims of Polynices--
like an eagle screaming, winging havoc
over the land, wings of armour,
shielded white as snow,
a huge army massing,
crested helmets bristling for assault.
The effect of this simile is to describe the serious threat and danger that the army of Argos represented. The comparison of the armed forced to an "eagle screaming, winging havoc / over the land" serves to emphasise the fear that the army caused in the hearts of Theban citizens, and the reference to the "huge army massing" again serves to exaggerate the threat and numbers of the army. This of course makes their defeat at the hands of the Theban defence all the more glorious. The simile thus serves to describe the very real threat and danger that faced Thebes, which makes their victory all the more meaningful.