The possessive marker shows possession or ownership. Everybody's house suffered some damage. Today's kids are under much stress.
Possessives occur only with nouns and time expressions and indefinite pronouns.
A possessive never occurs with a verb. Last night, yesterday, today, this year, tomorrow, etc. These, however, are never used with an apostrophe. In most cases, the word in the possessive is followed by another noun. The only exceptions are business or restaurant names because the names that would be following are implied.