Critic speak is tough, but we've got you covered.
Quote :Textual and Literary Criticism
Because of the corrupting (if not the revising) process in manuscript transmission before the state of printer's copy is reached, and because of the corrupting influence of the transmission into print of this copy, the recovery and authentication of Shakespeare's text must always proceed from multiple authority by eclectic means […] [T]extual bibliography takes as its end the logical scientific control of the eclectic method and the supplementing of the methods of literary criticism applied to choice readings. The control takes the form of requiring the purely critical judgment to operate within certain fixed bounds of physical fact and logical probability.
Many literary classics, including Shakespeare's plays, are available to us only in corrupt form. Shakespeare's plays, for example, were often transcribed by other people, years after Shakespeare's death, and we know these people made all kinds of mistakes in reconstructing his work.
The job of Textual Critics is to recover, as much as possible, the "original" literary work. Textual Critics interested in Shakespeare's Hamlet, for example, will want to arrive at the purest, cleanest, most authentic version of that play possible. And that, according to Bowers, can only be done by using an "eclectic" method.
That means that scholars can't rely on just one version of Hamlet to arrive at an authoritative edition of the play: they have to look at all the versions of Hamlet that are available, and they have to reconstruct an authoritative edition of the play out of all those versions. Textual Critics have to use their own judgment to decide which parts of each version are authentic and which parts aren't. Then they have to bring it all together to create an authoritative edition of the play.
Bowers was influenced by Greg's idea that you can't rely on just one copy-text to arrive at an authoritative edition of a literary work. The "eclectic method" is all about looking at different versions of a literary work and using all those versions to re-construct a super-duper authoritative version of that work.