Here are two entirely different uses of the term "dissociation of sensibility":
1. In his essay on The Metaphysical Poets, Eliot speaks admiringly of a sensibilty, a unified sensibility where thoughts and feelings are unified and do mutually reinforce each other (as in Donne and the Jacobean dramatists) -- and he speaks of a subsequent "dissociation of sensibilty" from which, he complains, we have not recovered.
      Tennyson and Browning are poets, and they think; 
      but they do not feel their thought as immediately as 
      the odour of a rose. A thought to Donne was an experience; 
      it modified his sensibility. When a poet's mind is perfectly 
      equipped for its work, it is constantly amalgamating 
      disparate experience; 
     The sentimental age began early in the eighteenth century,
     and continued. The poets revolted against the ratiocinative, 
     the descriptive; they thought and felt by fits, unbalanced; 
     they reflected. In one or two passages of Shelley's Triumph 
     of Life, in the second Hyperion there are traces of a struggle 
     toward unification of sensibility.
    "Jules Laforgue, and Tristan Corbiere in many of his poems, 
     are nearer to the 'school of Donne' than any modern English poet. 
     But poets more classical than they have the same essential quality 
     of transmuting ideas into sensations, of transforming an observation 
     into a state of mind."
Here, poets who do not display a unified sensibility in their work are not suffering from any medical condition of which Janet speaks.
2. Janet's term "dissociation of sensibility", on the other hand, has to do with a personality disorder -- a medical condition of a split in personality where one person experiences being more than one person.
  Eliot, and many other modernist writers, who were familiar with this medical
condition utilized it as a literary device to project dissociated selves of a literary
personae -- such as the projection of a part of oneself as another person, as visualized by the poet in Prufrock's Pervigilium.

--- On Thu, 5/6/10, Nancy Gish <[log in to unmask]> wrote:

From: Nancy Gish <[log in to unmask]>
Subject: Re: TS Eliot: The Metaphysical Poets
To: [log in to unmask]
Date: Thursday, May 6, 2010, 11:57 PM

Since I was said not to have given my own meaning, I am quoting myself in brief excerpts from a paper given in Florence. The following are two excerpts from a paper given but not yet published. so it is not to be quoted without permission.  This is a brief summary, but I was able to trace Eliot's use of this term in many texts where it clearly is connected with the then-common psychological term.  It is not simply an obvious use of the general meaning of "dissociate," nor is it something Eliot was not very familiar with.  For example, The Varieties of Metaphysical Poetry is clearly an allusion to William James's The Varieties of Religious Experience, which Eliot read and annotated.
In the late 19th and 20th century, a dominant medical concept was Pierre Janet's description of hysteria as always a form of dissociation or "a form of mental depression characterized by the retraction of the field of personal consciousness and a tendency to the dissociation of ideas and functions that constitute personality" (Gish 111).[i] It may take many forms, including amnesia; numbness; anaesthesia of all senses; aboulia or loss of will (which Eliot claimed as his own emotional problem); depersonalization, in which the subject experiences the self as unreal or detached from experience or even dead; derealization, in which the external world seems "unreal"; or the extreme form of the double (or dédoublement) in which "a person may actually perceive and even interact with an external double of him-or herself," including dual personality (Gish109).  
In his analysis of The Waste Land as an hysterical text, Wayne Koestenbaum opened up our reading to the ruptures, sexual anxieties and language dysfunction in what had increasingly been read as a unified mythic vision of the modern world.  But Eliot's own language, personal experience, and representations of dissociation suggest that the text's hysteria is more fully understood through Janet than Freud.  It is useful, I think, to note that Eliot went to Roger Vittoz after consulting several friends, that Vittoz's analysis of neurasthenia uses a model comparable to Janet's, and that Eliot specifically claimed in a letter to Sydney Waterlow that Vittoz was not a psychoanalyst "but more useful for my purpose." (L1 495) At this point, December 1921, he was in Lauzanne, "feeling much better," and "trying to finish a poem.

  [i] I have discussed in detail Eliot's knowledge of Janet and use of Janet's concepts in relation to the "dissociation of sensibility."  See "Discarnate Desire: T. S. Eliot and the Poetics of Dissociation" in Works Cited for extended definition and commentary on these terms."