The verb to commemorate means to celebrate in speech or writing, to preserve in memory by some celebration, or to be a memorial of someone/ something (Oxford English Dictionary.)

So a memorial service is held to commemorate the life and deeds of someone who has died; a biography could also be written for the same purpose. The most common use of the word is when appplied to statues, plaques or other public monuments which are put up to remind us of a person or event. For instance, all over Britain (and many other countries) you can see war memorials, put up to commemorate those who died in World War I.

The word comes from the Latin commemoratus, "made mention of." The noun form, much less used, is commemoration, and the adjective is commemorative (eg, "a commemorative plaque was put up outside the house where Famous Person X lived.") The person who carries out the action is called a commemorator, but again this is a rare word.