The "earth-walker" is the wanderer in the poem. He is literally wandering, looking for a new king and kinsmen to replace those he has lost. One of the themes of Old English poems such as this is the idea of ubi sunt. This means "Where are they who were once so glad to be alive?" The wanderer is in a state of severe melancholy. All those he once knew are now gone. He is left feeling barren and lonely. He dwells on the fact that everyone's life comes to an end. This sadness doesn't make him feel any better, but he accepts that this is the way the world works.
He has learned patience and wisdom through his lonely suffering. Since we all come to the same end, it is foolish to brag about one's life. It is certainly unwise to brag to Heaven if that is a potential final stop in the afterlife. (Here, the poet mixes Christian themes with the pagan culture.) He says it is foolish to not heed (pay attention to) his spleen (his melancholy or temper). In other words, he should pay attention to any sadness and loss because knowing this will give him the perspective and wisdom to deal with loss later in life. It will also allow him to be humble and appreciate the good times in his life while they are there to be experienced. It is better to be bold (brave) and accept the good and bad events in life. This is the path to wisdom and a better perspective on life and death.