Plato, I disagree. PhiloMath is clearly asking for definitions of the words "and" an "or". Since this is a "math help" forum, I presume he means their definitions as connectors in symbolic logic.
"And" is a connector such that the two statements P, Q are both true, then "P and Q" is true. Under any other conditions, "P and Q" is false.
"Or" is a connector such that if the two statements P, Q are both false, then "P or Q" is false. Under any other conditions, "P or Q" is true.
AND and OR, usually capitalized, are Boolean logical operators. AND for association, OR for alternate.
Examples: you ask for a computer AND a printer, means you will not accept the one withour the other, a computer OR a printer means you will accept either one. Of course if you are given the other one for free you will be happy.
In programming, these operators are used in IF statement, or a logical statement. If the logical statement is satisfied, the program bypass the next statement to a referenced label.
Boolean logical operators
Like HallsofIvy said:
"And" is a connector such that the two statements P, Q are both true, then "P and Q" is true. Under any other conditions, "P and Q" is false.
"Or" is a connector such that if the two statements P, Q are both false, then "P or Q" is false. Under any other conditions, "P or Q" is true.