verb (used without object)
to ramble without a definite purpose or objective; roam, rove, or stray: to wander over the earth.
to go aimlessly, indirectly, or casually; meander: The river wanders among the rocks.
to extend in an irregular course or direction: Foothills wandered off to the south.
to move, pass, or turn idly, as the hand or the eyes.
(of the mind, thoughts, desires, etc.) to take one direction or another without conscious intent or control: His attention wandered as the speaker droned on.
to stray from a path, place, companions, etc.: During the storm the ship wandered from its course.
to deviate in conduct, belief, etc.; err; go astray: Let me not wander from Thy Commandments.
to think or speak confusedly or incoherently.
(of a person with a mental disorder or cognitive impairment) to move about or walk in a seemingly aimless or random manner.
verb (used with object)
to travel about, on, or through: He wandered the streets.
Mechanics. the drift of a gyroscope or a similar device.

before 900; Middle English wandren, Old English wandrian (cognate with German wandern), frequentative of wendan to wend; see -er6

wanderer, noun
outwander, verb (used with object)

1. range, stroll. 2. saunter. 6. swerve, veer. 8. ramble, rave.
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
wander (ˈwɒndə)
1.  (also tr) to move or travel about, in, or through (a place) without any definite purpose or destination
2.  to proceed in an irregular course; meander
3.  to go astray, as from a path or course
4.  (of the mind, thoughts, etc) to lose concentration or direction
5.  to think or speak incoherently or illogically
6.  the act or an instance of wandering
[Old English wandrian; related to Old Frisian wandria, Middle Dutch, Middle High German wanderen]
adj, —n

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Word Origin & History

O.E. wandrian "move about aimlessly, wander," from W.Gmc. *wandrojan (cf. O.Fris. wondria, M.L.G., M.Du. wanderen, Ger. wandern "to wander," a variant form of the root represented in O.H.G. wantalon "to walk, wander"), from base *wend- "to turn" (see wind (v.)). In ref. to
the mind, affections, etc., attested from c.1400. The Wandering Jew of Christian legend first mentioned 13c. (cf. Fr. le juif errant, Ger. der ewige Jude).
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
Scores of backpackers, boaters, and private pilots will wander off course this
  month and get lost.
Before proceeding to the next paragraph, let your mind wander wherever it wants
  to go.
Because it is selectively managed and visitors are invited to wander about,
  this forest is actually a garden.
People reported being happiest when engaged in what they were doing versus
  allowing their minds to wander.
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