The Collaborative International Dictionary of English v.0.48:

Explain \Ex*plain"\ ([e^]ks*pl[=a]n"), v. t. [imp. & p. p.
   Explained([e^]ks*pl[=a]nd"); p. pr. & vb. n. Explaining.]
   [L. explandare to flatten, spread out, explain; ex out +
   plandare to make level or plain, planus plain: cf. OF.
   esplaner, explaner. See Plain,a., and cf. Esplanade.]
   1. To flatten; to spread out; to unfold; to expand. [Obs.]
      [1913 Webster]

            The horse-chestnut is . . . ready to explain its
            leaf.                                 --Evelyn.
      [1913 Webster]

   2. To make plain, manifest, or intelligible; to clear of
      obscurity; to expound; to unfold and illustrate the
      meaning of; as, to explain a chapter of the Bible.
      [1913 Webster]

            Commentators to explain the difficult passages to
            you.                                  --Gay.
      [1913 Webster]

   To explain away, to get rid of by explanation. "Those
      explain the meaning quite away." --Pope.

   Syn: To expound; interpret; elucidate; clear up.
        [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Explain \Ex*plain"\, v. i.
   To give an explanation.
   [1913 Webster]

WordNet (r) 3.0 (2006):

explain
    v 1: make plain and comprehensible; "He explained the laws of
         physics to his students" [syn: explain, explicate]
    2: define; "The committee explained their plan for fund-raising
       to the Dean"
    3: serve as a reason or cause or justification of; "Your need to
       sleep late does not excuse your late arrival at work"; "Her
       recent divorce may explain her reluctance to date again"
       [syn: excuse, explain]

Moby Thesaurus II by Grady Ward, 1.0:

149 Moby Thesaurus words for "explain":
   absolve, account, account for, acquit, aid, allegorize, analyze,
   answer, bottom, break down, clarify, clear, clear the way,
   clear up, condone, construe, crack, cry sour grapes, debug,
   decipher, decode, define, delineate, demonstrate, demythologize,
   describe, destigmatize, detail, disclose, discourse, disentangle,
   divine, do, do justice to, dope, dope out, ease, elucidate,
   enlighten, euhemerize, exculpate, excuse, exemplify, exonerate,
   expedite, explain away, explicate, exposit, expound, extenuate,
   facilitate, fathom, figure out, find out, find the answer,
   find the solution, get, get across, get over, get right,
   give reason for, give the meaning, grease, grease the ways,
   grease the wheels, guess, guess right, harangue, hasten, have it,
   help along, hit it, hold forth, illuminate, illustrate, interpret,
   justify, lecture, legitimate, legitimatize, loose, lubricate,
   make clear, make it clear, make out, make plain, make way for,
   moralize, oil, open the lock, open the way, open up, palliate,
   pave the way, plumb, point a moral, popularize, preach,
   prepare the way, psych, psych out, purge, put across, put over,
   puzzle out, quicken, rationalize, ravel, ravel out, read a lesson,
   rehabilitate, reinstate, remove friction, resolve, restore, riddle,
   run interference for, sermonize, shed light upon, show, show how,
   show the way, simplify, smooth, smooth the way, soap the ways,
   solve, sort out, speed, spell out, throw light upon, unbar,
   unblock, unclog, undo, unfold, unjam, unlock, unravel, unriddle,
   unscramble, untangle, untwist, unweave, vindicate, vulgarize,
   warrant, work, work out