From Wikipedia...

The term Eskrima is the Filipino spelling which comes from the Spanish word esgrima, "fencing". Arnis is thought to derive from the phrase arnÚs de mano, Spanish for "harness of the hand". The origin of the name Kali is not certain, although some suggest it is related to the traditional weapon called a kris, keris, or kalis. Another explanation is that the word is a portmanteau of the Filipino words kamot, or kamay meaning hand or body, and lihok, meaning motion. This explanation may be a more recent innovation, retroactively fitting an acronym to the existing name.

Also, this article by Bot Jocano, on "Arnis: A Question of Origins", might help: