Depiction of Lord Kalki on a white horse with a sword in hand allegorically means that Kalki Avatar would be one without precedent except Lord Krishna. The white horse symbolizes truthfulness which shall be the main strength of Kalki avatar. A follower of truth from beginning of life, Kalki avatar would rule the world with ruthlessness unprecedented.
Advent of an avatar can be equated to Judgement Day. Time for dillydallying tactics would have become passé. Justice would be served right on the moment, at times in minutes. The waiting period for getting justice would practically reduce to zero. No matter where the crime occurs, justice would be delivered within an hour.
Kalki avatar is a deadly combination of an enlightened one like Mahavira, Gautama Buddha Jesus Christ or Prophet Mohammed and Chanakya (the most able administrator in the entire history of mankind). To save his countrymen and soldiers from extreme hardships, Chanakya got 100 kings eliminated in one night. Kalki avatar has the capability to eliminate 5000 chieftains in one night.
Even God Almighty looks forward to the day when an avatar advents on mother earth for the day of the judgement brings peace all around.
The sword in hand of Kalki avatar means instant justice would be delivered to all throughout the world. None could escape the eyes of Kalki avatar. The ferocity, ruthlessness with which Kalki avatar administers justice would be a thing to reckon for times to come.