In ancient Italy, a "son of Italy" and his bride once attended a show. Due to her youth, beauty, and clothing, the young bride attracted a lot of attention.
Unfortunately, "a prop gave way" and the stage fell apart, striking the bride terribly. However, when everyone rushed to help her, they pulled back her clothes to find only "a robe of sackcloth" next to her smooth white skin.
The poem then describes her as a poet's muse, young and radiant on the outside, but containing an unsightly plainness within.
In order to fully understand this poem, it is important to know the definition of "austerity." When something is "austere," it has a simple and plain quality, and "austerities" are actions taken in order to live in a simple and plain way. In other words, it is a stark contrast to luxury or notable beauty - where the young bride seemed gorgeous, the sackcloth robe within is austere, unremarkable except for its plainness.
Understanding that definition, it is clear that Arnold has a mixed feeling about poetry (which can easily to read to represent all art in this poem). While he acknowledges that poetry can be outwardly beautiful and ornate - after all, it superficially boasts precise word choices, lovely language, and emotional expressions - he also believes that those elements are only disguises. Some poetry can be as austere or banal as a sackcloth robe, functional at best. In other words, a gorgeous poem might sometimes be disguising only a simple idea.
The poem then implicitly charges us to look closer at both art and life. The woman in this poem might be nice to admire, but all that really matters to whomever she loves is what she is like within. Similarly, Arnold suggests we can be seduced by the flowery language some poetry uses, while unaware that we are only celebrating banality. If you can see past the guise, you will be able to determine whether a poem is worth reading.
The stage works as a symbol to illustrate this point. The artistry that everyone has come together to witness falls apart, revealing the truth. In the same way that the stage play is only made of machinery and props, so is poetry only made of words. The only thing that truly recommends art outside this superficial, seductive outside is what the poet or writer has to say.
This poem is structured as a sonnet: a fourteen line poem format that originated in Italy. While Shakespeare is arguably the most famous of sonnet writers, Arnold uses a different form than he does. This poem is organized into two stanzas of four lines, and two stanzas of three lines. Sonnets often feature a very distinct shift in mood, tone, or events within the course of the poem; in this case, the very obvious shift occurs between the four line and three line stanzas, when the props fall on the bride, and her guise is revealed. To turn Arnold's point onto his own work, however, what matters most is what he is saying, and not the way in which he says it.