Wow! It must be hard studying the poetry of Emily Dickinson if English is not your first language. Good on you for doing this! Well, if we think about the last two lines, they of course relate to the rest of the poem and the way that the soldier who is described as "defeated--dying" can hear the sounds that the victorious army are making as they celebrate their success. Note what the last two lines say:
The distant strains of triumph
Burst agonised and clear!
The "distant strains" here are the distant sounds of triumph that "burst" upon the dying soldier. Of course, because he is dying in failure, they burst "agonised and clear" to highlight his lack of victory. However, let us not forget the central irony. It is this dying, defeated soldier that will understand success better than the victorious army, Dickinson suggests, as it is he who desires it so badly that "counts" success to be "sweetest." I hope this helps!