Whatever is used in fire you shall pass through fire and then it will be clean; it must also, however, be cleansed with sprinkling water, and whatever is not used in fire you shall pass through water. (Numbers 31:23)
There are two separate areas of Jewish law which pertain to this verse. The first is the law of hechsher keilim, the cleansing of forbidden foods from kitchen utensils.
The Gemara (Pesachim 44b) explains that when food is cooked, its taste is transferred into the utensils used in the process. If the food is non-kosher, the taste transferred will also be non-kosher and the utensil will be rendered unfit for use in a kosher kitchen.
Our verse explains that for the utensil to become kosher again, it must go through the same process used in the cooking of the non-kosher food. Once cleaned, if the non-kosher food had been grilled with fire, the utensils used can only be purified with fire. If the food was boiled, the utensils used must be purified with boiling water.
The second principal is the law of tevilat keilim, which dictatesthat kitchen utensils (except those made from plastic or wood) acquired from non-Jews must be immersed in a mikveh (ritual bath) before use in a kosher kitchen in order to carry out a process of spiritual purification.
The first law of kashering kitchen utensils achieves a physical change in the utensil whereas the process of tevilah – immersion in a mikvahi, does not change the physical properties of the utensil at all.
The Gemara (Rosh HaShannah 17a) compares a sinner to a blackened pot. The process of teshuvah – repentance (lit. return) is a two stage process. First one must desist from the sinful act and confess which is similar to the process of hechsher keilim yielding a noticeable change in behaviour. Secondly the sinner must begin to make internal changes to their character to safeguard themselves from repeating the sinful act. This is similar to tevilat keilim which does not generate a physical change, but represents a profound spiritual transformation.