A pot which has had hot food in it within the last 24 hours is called a ben yomo. If it did not have hot food in it within 24 hours, it is called an eino ben yomo. The taste of food that was absorbed in a pot changes from within 24 hours to after 24 hours. During the first 24 hours that the food was there, the taste is still fresh and tastes good. After 24 hours elapsed, the taste is weakened and does not taste good anymore. The Gemara in Avoda Zara (75b) brings a dispute whether something which imparts a bad taste (noten taam lifgam) from a food that was prohibited can forbid kosher food or not. We rule that the bad taste of forbidden food does not prohibit kosher food. The Gemara asks: if taste goes bad after 24 hours and we go by the opinion that this taste would no longer prohibit food it goes in to, why did the Jews have to kosher all the pots they got from Midian? The pots surely were not used in the last 24 hours and would therefore not have caused any food subsequently cooked in them by the Jews to be forbidden. The Gemara answers that the only pots that the Torah required them to kosher were pots that indeed had been used in the past 24 hours. The Gemara adds that even though the Torah permits using the pots after they have not been used for 24 hours, it is still initially prohibited to use any pot that had non-kosher food cooked in it. After the fact, food cooked in the pot would usually be permitted. From this Gemara we learn the rule of ben yomo, that only a ben yomo pot has the power to prohibit food which was cooked in it.
We start the clock on the 24 hours as soon as the food in the pot has cooled and is no longer yad soledet bo – the temperature at which an infant gets scalded (about 114 degrees Fahrenheit). The Shulchan Aruch (שו”ע יו”ד סי’ קג סעיף ז) writes that any food cooked in a non-kosher pot which was eino ben yomo is permitted to be eaten after the fact, provided that the pot was clean. If the pot had non-kosher food still stuck to the walls, it could make the kosher food prohibited.
Even though the food is permitted after the fact, the eino ben yomo pot still must be koshered, and it is forbidden to use the pot deliberately because it has the taste of forbidden food absorbed in the walls. If a meat pot that was an eino ben yomo was used for dairy (or vice versa), the food cooked in the pot is permitted after the fact, but the pot needs to be koshered before continued use, since it now has taste from both meat and dairy. One should preferably avoid washing the pot in the kitchen sink because the pot now has the status of both meat and dairy, and one should use a separate sponge for the pot when cleaning it before koshering.