Put simply, the night has been stormy but now in the morning it's a beautiful day. The contrast is stated directly and without intricacies or elaboration:

There was a roaring in the wind all night,
The rain came heavily and fell in floods,
But now the sun is rising calm and bright;
The birds are singing in the distant woods.

These are just the first four lines of the poem. From this point Wordsworth does elaborate on his description of the calm morning in which,

All things that love the sun are out of doors;
The sky rejoices in the morning's birth;

And:

I saw the hare that raced about with joy;
I heard the woods and distant waters roar;

At first the speaker is completely gladdened, and states that:

My old remembrances went from me wholly,
And all the ways of men, so vain and melancholy.

Despite the beauty of nature, the poet's positive mood doesn't last. From much, if not most, of his verse, one sees that Wordsworth was a man prone to periods of depression. He identifies this as basically the fate of artists in general:

We poets in our youth begin in gladness,
But thereof in the end come despondency and madness.

It's as if the joy in nature, and the reflection that he has spent his life in "pleasant thought," are a signal that something bad is to happen—that the joyful mood cannot, or should not, be allowed to last. The speaker thinks about the poet Chatterton, the "marvelous boy" (in Wordsworth's description), who killed himself at the age of 17 and became a symbol to the Romantic age (as other similar poets and composers did) of the artist's tragic fate, dying young and unappreciated.

The appearance of the leech-gatherer is emblematic of the dichotomy that persists in life between the opposite moods of joy and sadness, or even terror. Against this backdrop of the beauty of nature a wreck of a man is sifting the water of a pond for leeches. Though it's not stated directly, the speaker inwardly compares his own self-created troubles with those of a man genuinely in need, and "laughs himself to scorn" as he reflects upon how "firm a mind" the old man has.

As always with Wordsworth, the strength of the poem lies chiefly in the simple and direct quality of his language, his brief descriptions of the contrasts within nature, between the stormy night and beautiful morning, and the mirror of those contrasts in his own mind. Wordsworth was one poet who (as he intended) was able to write the way people actually talk—without "poeticisms" but still poetically.