As a noun, honour (British spelling) or honor (American spelling) means honesty and fairness. To be honoured is to be a source of credit and distinction, and one who is honoured is held in high esteem and enjoys glory as a person of integrity. A woman's honour is her chastity or virginity. Judges and mayors are referred to as "Your Honour" in Britian and Canada, "Your Honor" in the States. Having the honour to do something means that one is privileged to be associated with something, as in "I have the honour of belonging to the Content Rescue Team". (I do!) Honours degrees in university are conferred upon excellent students. To do the honours means to preside over something, such as the pouring of the tea or carving the Thanksgiving turkey. In bridge and whist, and probably other card games as well, the hounour card is usually the highest trump card.
As a verb, to honour means to hold someone or something in respect and confer distinction on them. The war dead are often honoured with memorials and wreaths. To honour something is to accept it as valid; a business can honour a credit card or a personal cheque. In square dancing, to honour someone means to salute them with a bow.