"Consolation" is, primarily, a poem about the effects of time and its ruthlessness.
The speaker of "Consolation" begins by describing his dejection. However, while he sits and languishes, time is running on everywhere else. To illustrate his point, he describes various places where various things are happening: the sun shines bright on roofs and terraces in Asia, marbles in a gallery by the Tiber river "hold their pure Muses," a beggar seeks aid in an African city, and a robber wanders through the desert.
The second half of the poem focuses on a more specific scene: two young lovers, entranced by each other's presence, plead for the Goddess of Destiny to prolong the present so that their time together can last forever. But the goddess shakes her head and time moves on, so that their hour is soon passed.
The speaker acknowledges that, had the goddess lengthened their hour, she would have increased their happiness, but prolonged someone else's distress. While they may have wanted the hour to continue, miserable mourners elsewhere would have desperately wanted it to end.
At the end of the poem, the speaker observes that time is different for everyone, yet partial to no one.
This poem is extremely potent, and its theme is universal. Many of Arnold's poems about the rise of modernism and the New Age are harder for us, as students in the 21st century, to relate to. But the questions Arnold raises about time here are ones any person has asked to some extent. We have all wanted to change time in some way or another.
To best explore the theme, Arnold personifies both time and destiny, the latter as a goddess. Though he was often skeptical of religion, faith was important in Arnold's life. Many of his poems visualize heaven as a place of transcendent serenity, and he clearly believed in a force that controlled time on earth. By personifying destiny here, he subtly places an emphasis on faith, since he very much believed that it was an essential component of life. We also like the idea that someone has control over time, even if this someone is not human. Of course, that idea has a certain pessimism as well - since someone else has control, it means we do not have control. The poem has a mildly desperate air, rather than being a detached consideration of the subject, because of this helplessness.
There are two particularly unique ways Arnold emphasizes how small humans are in the face of time. Arguably the most interesting is the idea that our own desires will always conflict with someone else's. The example of the lovers - who wish to prolong a moment unaware that other miserable people want that moment to end - suggests how little perspective we truly have on the larger course of time and the world. We are aware only of what and who we are (like the islands of "To Marguerite: Continued"), and lack any greater knowledge of how time is working in the large sense.
This sense of distance between people runs throughout the whole poem, as Arnold wisely brings us to different corners of the globe. This approach both suggests lives totally divorced from one another and further emphasizes the universality of time. As usual, he uses a lot of visual imagery: mist clogging the sunshine, the yellow Tiber, sun-proof alleys, a sand-hemmed city of Africa. This makes time seem like a visual entity, rather than just an abstract idea. We can see the effects of time in the world around us, in the way cities and people and weather changes. It is more than just a concept; it is the unifying principle of all life, even though we are rarely aware of how it binds us.