From the context. First we need to know that you seem to be talking of regexes, because a carat can have even more meanings, e.g. exponentiation in several programming languages, upper case conversion in certain shells' "Case Modification Parameter Expansion", or used to produce characters like ‚ in the French locale.
In regexes, if used as the first character in a matching pattern, it anchors the pattern at BOL. If not the first character, it is treated as is, i.e. there must be a carat in the text to match the carat in the regex.
In a bracket expression, if the list begins with '^', it matches any single character not from the rest of the list.
In a [character set] if the first character is ^ it means NOT the following character set. ^[^nN] means at the beginning of the line there must be a character that is not n or N.
BTW please always put grep regular expression in "quotes" or 'quotes'. Then it is guaranteed that the shell does not try to make any expansion but passes the string to grep as is.