EDIT The Staff of Hermes represents a staff with two wings and with two snakes twined symetrically around it. It is associated with trade and the Greek god Hermes.
A herald (caduceator) carried the caduceus (heraldstaff) as a mark of his mission. The best known carrier of the staff was Hermes who had wings on his feet, hence the wings on the staff.

The symbol evolved about 2600 B.C. and was used by the Greek priests. The alchimists of the medieval times liked to use it which makes it popular today for occult purposes.
 
EDIT Caduceus vs. Aesculapius
The Caduceus looks very similar to the Staff of Aesculapius and the two are frequently confused with each other. The Staff of Aesculapius has no wings and just one snake. In Unicode 4.1, which was published recently, the Staff of Aesculapius is encoded at U+2695.
 
ADD NEWSIMILAR CHARACTERS
01 CODE POINT VALUE: : : : : 2624
02 NAME (UNICODE NAME) : : : CADUCEUS
03 GENERAL CATEGORY: : : : : Symbol, Other
04 COMBINING CLASS : : : : : Spacing, split, enclosing, reordrant, and Tibetan subjoined
05 BIDIRECTIONAL CATEGORY: : Other Neutrals
06 DECOMPOSITION MAPPING : : -
07 DECIMAL DIGIT VALUE : : : -
08 DIGIT VALUE : : : : : : : -
09 NUMERIC VALUE : : : : : : -
10 MIRRORED: : : : : : : : : No
11 UNICODE 1.0 NAME: : : : : CADUCEUS
12 ISO 10646 COMMENT FIELD : -
 
13  UPPERCASE MAPPING : : : : -
14 LOWERCASE MAPPING : : : : -
15 TITLECASE MAPPING : : : : -
16 DECIMAL VALUE : : : : : : 9764
17 UTF-8 HEX VALUE : : : : : 0xE298A4
18 UTF-16 HEX VALUE: : : : : 0x2624
19 UTF-32 HEX VALUE: : : : : 0x00002624
20 XHTML : : : : : : : : : : &#9764
21 BLOCK : : : : : : : : : : Miscellaneous Symbols
22 PLANE : : : : : : : : : : Supplementary Ideographic Plane (SIP)
23 STROKE NUMBER : : : : : : -
24 RADICAL : : : : : : : : : -
 < CHARACTER >  BLOCK PROPERTIES
U+2624 CADUCEUS
DEUTSCH : ENGLISH