Logical fallacy refers to fallacious reasoning, or in other more simpler terms, a fallacy in an logical argument. There are many logical fallacies and some examples are below:
~ argument to the man. You attack a person verbally as opposed to their argument (i.e a person attack).
argument ~ setting an argument up and knocking it down, called a straw man because it's based on a misconception of the argument proposed to you (normally done purposely).
Argument from authority
~ when you call upon a higher body (i.e a government, a community, someone with credentials) to support your claim (i.e "Stephen Hawking is an atheist and that therefore makes atheism correct because Hawking is an intelligent man!"). Has no place in science as the personal views of an individual are meaningless.
Argument from numbers
~ refers to using the number of supporters for something to support the claim (i.e "Billions of people smoke! It's acceptable!").
No true Scotsman
fallacy ~ logical fallacy used when someone holds that someone isn't a member of (insert group here) because it doesn't adhere to their personal view (i.e "Stalin and Mao weren't atheists because they were elitists and in my world-view, atheists can't be elitists!").
Moving the goalposts
~ logical fallacy used when someone attempts to shift their argument to something else when their original one is knocked down or when evidence is presented and it's dismissed with new evidence demanded (i.e "I don't care that you just provided me with a list of scientists who claim to believe in God as I originally asked you, prove to me that they aren't lying!").