When a food is forbidden to eat, the taste of the food is also forbidden (Chullin 98b). The Gemara in Pesachim (44b) brings two sources for this. The first source is learned from a nazarite, one who is forbidden to eat grapes. The Torah says that a nazarite cannot eat anything in which grapes have soaked. The Gemara learns from this that since a nazarite is forbidden to eat anything that has even a taste of grapes, it must be that the taste of a food is equivalent to the food itself. A second source is from the story of the Jewish nation conquering the nation of Midian. After the battle was won, the Jews took the pots and pans that belonged to the Midianites. The Torah records that Elazar Hacohen commanded them to kosher all the utensils they had taken. The Gemara explains that when cooking food in the pots that they took from Midian, the pots would impart non-kosher flavor to the kosher food, making the food not kosher.
There is a dispute between Rashi and Tosfot whether the rule of taam k’ikar is a biblical prohibition, or a rabbinic prohibition. Rashi rules that it is only a rabbinic prohibition, while Tosafot rules that it is a biblical prohibition. One difference that comes out of this dispute concerns a mixture of forbidden food in a liquid mixture of another food whose taste was permitted. If there was definitely more permitted food but we don’t know whether there is sixty times the volume of the forbidden food, then according to Rashi it is permitted to eat the food. According to Tosafot it is forbidden. The reason for this is that since according to Rashi this is a rabbinic prohibition, when we are uncertain about the status of a rabbinic prohibition, we are lenient. Tosafot rules that this is a biblical prohibition, and therefore when we are uncertain what to do, we have to be stringent. We rule like Tosfot that taam k’ikar can create a biblical prohibition.
There are two ways to impart taste to a food, and both would make the food receiving the flavor prohibited. One way is to actually dissolve the food that is forbidden into the food that is permitted. For example, if one mixed broth from non-kosher soup into a kosher soup. The other way is to absorb flavor without the actual forbidden food ever getting mixed in. For example, cooking kosher food in a non-kosher pot.
Since taste is equivalent to the food itself, the taste of forbidden food can make a food forbidden. For example, the taste from milk that got absorbed in meat would forbid the meat. The same holds true in regard to a pot. If meat was cooked in a pot and the pot absorbed taste from the meat, then anything subsequently cooked in the pot would receive the meat flavor from the pot. Therefore, if you cooked dairy in the pot, it would be considered as if you cooked milk and meat together.