The origins of this tradition are lost to time, like those of so many other customs, and several hypotheses exist to explain the gesture. The most common explanation, and the most symbolical (and superstitious) as well, is that offering a knife, or any sharp object, might ''sever'' the link of friendship between the person who gives it and the person who receives it. In other words, a coin is given in exchange for a knife in order not to ''sever'' friendship.
Symbolically, the knife is therefore ''sold'', rather than given. Even though ''sold'' may not be the most accurate description: mostly because tradition dictates that the coin should be of the lowest possible value, in order to emphasize that it is not a commercial but a symbolical gesture. The symbol derives from the fact that a coin cannot be cut nor divided.
“Giving this object therefore affirms that the friendship between both parties is just as impossible to sever. Which is why some slightly different traditions (particularly in the USA) require the person who gives the knife to also give the coin.”
In any case, it is a way to proclaim that friendship will not be ''cut'' by the offered blade. And whether you believe in superstitions or not, reaffirming the strength of a relationship is just as valuable as the gift itself.