The output of an AND gate is true only when all of the inputs are true. If one or more of an AND gate's inputs are false, then the output of the AND gate is false.
An OR gate is when either of the values can be true, and the output shall always be true in that instance. The images below shows what the OR gate looks like, and the table shows all possible outcomes.
A NOT gate outputs the opposite of what is inputted. The image below shows a NOT gate, as well as all possible outcomes.
A NAND gate is an inverted AND gate meaning the inputs will cause an inverted outcome, so having no input will cause an output of 1, which is the opposite of an AND gate, which would be 0.
A NOR gate is an inverted OR gate, so any input will cause an output of 0 and this is the opposite of a regular OR gate, which would give an output of 1.
An XOR gate is a variation of the OR gate, however, out of its two inputs, it will only give an output of 1 if only one of the inputs is 1, and an output of 0 if both are off or if both are on.