The Collaborative International Dictionary of English v.0.48:

Explore \Ex*plore"\, v. t. [imp. & p. p. Explored; p. pr. &
   vb. n. Exploring.] [L. explorare to explore; ex out+plorare
   to cry out aloud,prob. orig., to cause to flow; perh. akin to
   E. flow: cf. F. explorer.]
   1. To seek for or after; to strive to attain by search; to
      look wisely and carefully for. [Obs.]
      [1913 Webster]

            Explores the lost, the wandering sheep directs.
                                                  --Pope.
      [1913 Webster]

   2. To search through or into; to penetrate or range over for
      discovery; to examine thoroughly; as, to explore new
      countries or seas; to explore the depths of science.
      "Hidden frauds [to] explore." --Dryden.
      [1913 Webster]

WordNet (r) 3.0 (2006):

explore
    v 1: inquire into; "the students had to research the history of
         the Second World War for their history project"; "He
         searched for information on his relatives on the web";
         "Scientists are exploring the nature of consciousness"
         [syn: research, search, explore]
    2: travel to or penetrate into; "explore unknown territory in
       biology"
    3: examine minutely
    4: examine (organs) for diagnostic purposes

Moby Thesaurus II by Grady Ward, 1.0:

51 Moby Thesaurus words for "explore":
   beat the bushes, burrow, delve, delve into, dig, dig into, examine,
   fathom, forage, frisk, go into, go through, hunt, indagate,
   inquire into, inspect, investigate, look around, look into,
   look round, look through, nose around, observe, peer into, plumb,
   poke, poke around, poke into, probe, prospect, pry, pry into,
   quarry, question, research, review, root, scrutinize, search,
   search into, search through, sift, smell around, sound, study,
   survey, test, tour, travel, traverse, try