Lots of people seem to confuse the words affect and effect, probably because they sound very similar, if not entirely the same out of some mouths. One's a verb, they'll recall, and one's a noun, but which is which? And eventually people mostly figure it out: effect is the noun, and affect is the verb. Remember, Affect Verb, Effect Noun: RAVEN.
But actually, both words can be either a noun or a verb! Taken from the dictionary of the almighty Google on 12 March 2016 (affect and effect):
affect1 /ə'fɛkt/ (verb) have an effect on; make a difference to. "the dampness began to affect my health"
affect2 /ə'fɛkt/ (verb) 1. pretend to have or feel (something). "as usual I affected a supreme unconcern" 2. use, wear, or assume (something) pretentiously or so as to make an impression on others. "an American who had affected a British accent"
affect3 /'æfɛkt, ə'fɛkt/ (noun) [PSYCHOLOGY] emotion or desire, especially as influencing behavior or action.
effect /ə'fɛkt/ (noun) 1. a change that is a result or consequence of an action or other cause. "the lethal effects of hard drugs" 2. the lighting, sound, or scenery used in a play, movie, or broadcast. "the production relied too much on spectacular effects" 3. personal belongings. "the insurance covers personal effects"
effect /ə'fɛkt/ (verb) cause (something) to happen; bring about.
Bluntly put, an affect is what a psychologist would say their patient has if they appear to be happy, or not emoting, etc. Note that most of the time, this is pronounced differently from the other versions: the first syllable is actually stressed, and the 'a' sound is /æ/ as in 'hat' instead of the usual /ə/ sound. The definition for to effect is pretty self-explanatory.
It should be noted that the other forms of affect and effect are not nearly used as frequently as the main two, so that's why it's more likely than not that correcting someone using effect as a verb is the right thing to do. However, you should be aware that people do use the other meanings.