There are two concepts in the Halacha of Bittul (nullification). One says that if there is an item that is Unkosher that falls into another item that is Kosher, and it is a mixture, and the Unkosher is one-sixtieth, it is nullified and you can eat the mixture even though it has the Unkosher in it. However, there is another Halacha along the same premise that says if Roiv (a majority) of the food is Kosher, then the Unkosher food is nullified. Wouldn't you know that from the fact that it is more than SIXTY?
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Sometimes rov is enough and other times we require shishim. See this chart for details but basically the only case l'halacha we will rely on rov is if no taste is transferred (yavesh byavesh) and taste the same (min bmino).
There are really two types of Bittul (nullification):
(There are way too many sources, but see the Taz YD 98:3 for a similar, succinct, and good enough summary.)
Please make sure to CYLOR before relying on these principles yourself, as there are many small details that can make a difference.
To quote myself:
The point of having 60:1 is generally just to guarantee there isn't any significant, discernible flavor, as is clear in YD 98:1 and other places.