Hugs and Kisses is a term for a sequence of the letters X and O, e.g. XOXO, typically used to express affection or good friendship at the end of a written letter or email.
It is debatable which letter represents which act. Some interpret X as the crossed arms of a hug and O as the puckered lips of a kiss. However, the interpretation assumed in the following, in which X represents the four lips of a kiss and O the four arms of a hug, is more common. For example the Oxford English Dictionary states that X is "used to represent a kiss, esp. in the subscription to a letter." [1]
Most celebrities these days will sign an autograph with "xoxo" and their signature to show love to a fan.
Additionally, there is a more simple interpretation, based on the pronunciation of the letters X (sounds like 'kiss') and O (sounds like 'hold', as in 'I hold you').
The use of XOXO goes back to the use of an X or cross, which was considered as good as a sworn oath in times before most people could write and therefore used the X in the same way a signature is used today — a mark of one's word.
An X at the end of a letter or document was often kissed as a seal of honesty, in much the same way one would kiss a Bible or kiss the fingers after making the sign of the Christian cross, thus the X came to represent a kiss in modern times.
The "X" was the ancient Paleo Hebrew letter Tav, and was a symbol of the Seal of Hashem (God) and it represented truth, completeness, and perfection.
The origins of the O as a hug are not generally known, although it is speculated that it may represent the arms wrapped around someone being hugged.