The theme of "hope," as presented in Addison's title, demonstrates the very essence of what can be found (or so we hope) in a child's life: when all things are possible, and the worries and struggles of adult life have not yet left one bruised and battered. In fact, the first line of "Hope" brings to mind the very image of bruising:
Our lives, discoloured with our present woes...
In this introductory phrase, the author is describing the negative effects of sorrow. "Present" (we can infer) points to the now—in one's adulthood. A comparison is evident with "discoloured" and "white." White is symbolic of purity or of newness. "Happier hours" refers to childhood.
May still grow white and shine with happier hours.
Addison is noting that while we sit under the weight of being an adult, one may still retreat in his/her memory to happier times. As a child, one need not (generally) be worried about paying bills, losing a job, struggling in relationships (such as with a spouse), or being disappointed by others or the world. For a child, there are scrapes and disappointments that can be comforted away, lasting only until something new captures the child's interest: for in this, a sad moment is forgotten, which is many times not the case for someone who is grown.
The next four lines describe the process of moving from the murky waters of adulthood into the pristine state of being a child. And whether or not there is truth to the memories of childhood—whether, in fact, the days of a person's youth were truly ideal—one's memory will often recall with clarity the good things, and this period in one's past seems so much more desirable than the present. Note the transition from the pain of the present day to the idyllic in the past, offered as a metaphor. Childhood is the "pure...stream;" dirty water is adulthood:
So the pure limped stream, when foul with stains
Of rushing torrents and descending rains,
Works itself clear, and as it runs refines,
till by degrees the floating mirror shines...
"Foul with stains / Of rushing torrents and descending rains" refers to the challenges of being fully grown. The "stains" and "torrents" bring to mind difficulties. The reader may consider the power of water—its ability to wear down rocks and pull away pieces of a shoreline. However, as the water moves—as a person travels back to his or her past—the liquid loses all that has contaminated it...just as one arrives in the past, where the difficulties of the present are lost. One's mind is "refined," and can see only a clear and mirrored surface, reflecting the best of times.
In that moment of transport, as Addison extends the metaphor, the water is not only clear (perhaps symbolizing the golden days of childhood), but specific details of that idyllic time also come to mind, as seen in the flowers growing on the shore. In taking this trip, Addison seems to infer that one can again (by retreating to the past) enjoy a sense of great possibilities ahead and perhaps envision a "new heaven"—the hope that things in adulthood will improve, just as a child imagined things would be on the morrow: for a new day held the promise of infinite possibilities. And in this way, life holds hope for those who can retreat to happier times and fill themselves with a sense that better days lay ahead.
Known for writing commentary and philosophy (among other topics), Addison addressed aspects of the human condition. Here, it is about holding on to hope.