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Etzem means what is inner and essential. In modern Hebrew, politicians will frequently say "etzem ha'inyan", which means roughly, "the essential fact of the matter", and is equally vacuous and clichéd. The word itself means bone, and we see the similarity to the now archaic English phrase, "the marrow of the matter".
Three times, the Torah uses the phrase "b'etzem hayom hazeh". It's sometimes translated as "on that very day", but we can see that the sense is more, "by virtue of the essential nature of that day". It occurs in Exodus 12:51 where God is described as taking Israel out of Egypt b'etzem..."the day on which we now celebrate the Seder"; then again in Leviticus 23:14 when the day of bringing the Omer offering is called b'etzem. And finally it is used twice about Yom Kippur, Leviticus 23: 29-30. The common understanding underlying these cases seems to be that the day itself is transformative. We may experience and re-experience this potential year on year.
Etzem meaning essential also has a place in yeshivish slang. Chaim Weiser gives the example: "It's less the taste of yeshivah food that bothers me than the etzem quality."