The Collaborative International Dictionary of English v.0.48:

January \Jan"u*a*ry\, n. [L. Januarius, fr. Janus an old Latin
   deity, the god of the sun and the year, to whom the month of
   January was sacred; cf. janua a door, Skr. y[=a] to go.]
   The first month of the year, containing thirty-one days.
   [1913 Webster]

   Note: Before the adoption of New Style, the commencement of
         the year was usually reckoned from March 25.
         [1913 Webster]

WordNet (r) 3.0 (2006):

January
    n 1: the first month of the year; begins 10 days after the
         winter solstice [syn: January, Jan]