The ebb tide is the tide that is receding, or the water that is being pulled back into the ocean. It is getting lower in its level, and withdrawing back and away from the shores of the beach. Considering the main theme of Arnold's poem, his focus on the dwindling or disappearing tide is consistent. Arnold holds a pretty pessmistic view of the world. He uses the receding ocean as a symbol for how he feels "the Sea of Faith" is too experiencing a "melancholy, long, withdrawing roar." He feels that goodness, faith, virtue and humanity is slowly withdrawing its beauty from the earth, just as the tide ebbs away. Goodness is ebbing, leaving behind, as Arnold states, only "ignorant armies clashing" and "struggle and flight."
Arnold's attitude that "peace," "love," "joy," "light," and "certitude" is slowly receding from the world matches his focus on the ebbing tide. He views the world's goodness as fading away, instead of flowing in and filling again. It's a rather dismal viewpoint, but happens to be the focus of his poem. He hopes that if he and his love are "true to one another," perhaps they can try to counteract the evil that is descending, but that is his only glimpse of hope in the poem.
I hope that helps a bit; good luck!
In the opening stanza of Arnold's poem, the sea is 'calm', it being 'full'. Later in the same stanza, the poet gives us the image of the endless backward and forward movement of the waves, 'the grating roar of pebbles' generating, 'with tremulous cadence slow', a melancholy music eternally audible.
Arnold dwells on the ebb tide in the 3rd stanza:
The Sea of Faith
Was once, too, at the full, and round earth's shore
Lay like the folds of a bright girdle furled.
But now I only hear
Its melancholy, long, withdrawing roar,
Retreating to the breath
Of the night wind, down the vast edges drear
And naked shingles of the world.
These lines refer to an allegorical 'Sea of Faith' which was, in the past, a mode of protection for the whole of mankind, like a rounded piece of clothing around the shores of life. That faith of the pre-Industrial days is now gone in the modern times of doubts, disputes, conflicts & controversies. The receding movement of the 'Sea of Faith' leaves back a barren, waste land, the world lying stripped naked. The image of the ebb tide thus signifies the crumbling of faith and its resultant spiritual vacuum.