In examining the lyrics of the song, in general, the speaker is calling on the chariot from the heavens to "carry me home." This is a call to the divine. The call to the chariot from above is a plea to the divine to send the vehicle to take the speaker out of the condition from which they exist. It is a call to transcend what is into what can be. In much the same way, the call to "carry me home" during the time of slavery can be a plea for the members of the Underground Railroad to rescue slaves who were singing for their freedom and improvement in their condition. The reference in slavery is a call to some external force to rescue the slave from the condition of American slavery in the South.
In both settings, the figure that is coming to carry the speaker "home" represents a form of deliverance from a condition of suffering and pain into a realm where consciousness is fundamentally better. The figures that are being asked to bring the chariot are external saviors. They represent a sense of hope and a form of liberation from the condition of pain and suffering that the speaker is enduring. Asking for the "sweet" chariot to "swing low" is a way to find liberation from a condition of what is into what can be.