"I felt a Funeral, in my Brain," like many of the Dickinson's poems, deals with the subject of death. In particular, she likes to deal with the subject of the moment of death and burial. For example, check out her poems "I died for Beauty – but was scarce" or Shmoop's analysis of "I heard a Fly buzz – when I died –". It seems that Dickinson was either afraid of death, or really curious about it, or maybe a mix of both. She seemed to believe that people went through death-like experiences throughout their lives. One of the central questions in this poem is whether death is a metaphor for some other experience.
The poem is written from the perspective of a dead person in a casket, and every detail of the poem can be explained along these lines.