In the first stanza of "The Relic," the speaker envisions his grave being disturbed. The speaker supposes that the grave digger (disturber) will notice that a "bracelet of bright hair" is buried with him. This hair symbolizes/is from the speaker's mistress. The speaker concludes with:
To make their souls at the last busy day
Meet at this grave, and make a little stay?
This refers to the Renaissance belief that on Judgment Day, souls would reunite with their bodies to experience the Resurrection. Consequently, the speaker's mistress would return to him to retrieve her hair and they would have a short reunion at the grave ("make a little stay.")
The second stanza proposes a different scenario. The speaker's grave is disturbed, but not on Judgment Day. Rather, it is some unspecified time in the future when religion has become misguided ("mass devotion"), having shifted focus to relics. Those who would worship he and his mistress, in such a time of mass devotion, would be seeking miracles. In the last two lines, the speaker claims he would explain miracles he and she performed when they were alive.
In the third stanza, the speaker tells of their miracles. They loved each other and it was platonic, chaste. Their love had nothing to do with sex or gender. It was beyond their understanding and had a spiritual quality:
First we loved well and faithfully,
Yet knew not what we loved, nor why;
Difference of sex we never knew,
No more than guardian angels do;
The speaker concludes by saying his mistress was also a miracle.
The poem mixes morbid imagery with ideal notions of love. A relic is something which survives the passage of time and usually the context, culture, and/or era from which the relic had emerged has been long forgotten. In other words, the relic may refer to the speaker and his mistress or their love. That is, upon discovering the speaker's grave (and the mistress' hair), future generations will admire the relic but not fully understand it. And, referring to the last stanza, this kind of ideal love is also too mysterious for the speaker to understand. He should exhaust all language in attempting to describe "what a miracle she was." Shifting the focus to the mistress herself, the miracle also can mean life. All of these examples suggest that love and life are abstract relics: concepts which survive the passage of time, relics which have existed for so long that we no longer remember (or simply cannot comprehend) how, when, and why such things emerged.