What is the exact definition of "Token?"

If you google define:token, you get (amongst others) the following two definitions that seem applicable:

• an individual instance of a type of symbol; "the word 'error' contains three tokens of `r'"
• something serving as a sign of something else

If you combine these two, you will land somewhere near what is commonly meant when talking about tokens in programming; a symbol representing something. Pretty vague, yes, but then it's used in many different contexts.

One example: you have an authentication system where a user logs on. When the system has authenticated the user, instead of repeating this process for every request, a token is created that represents the fact that the user is authenticated. This token is then used in subsequent requests. In this case the something is the fact the the user is authenticated, and the token represents this fact.

Tokens are: identifiers, keywords, literals, operators, and punctuators. But we can't consider White spaces and comments as tokens, though they act as separators for tokens.

In the compiler Lexical analyzer (or scanner ) : Reads the input stream and fuses characters of the source text into tokens of the language. Token : sequence of characters having a collective meaning. The character sequence forming a token is called the Lexeme.

this example might help
Consider the following assignment statement
newvalue = oldvalue + rate * 60
The lexical analyzer will generate the following tokens.

Token       Lexeme
Identifier  newvalue
assignop    =
Identifier  oldvalue
addop       +
identifier  rate
mulop       *
number      6