Feeling in laymen's terms is often associated with emotion. Feeling in MBTI terms is referring to rational thought processes. The irrational functions are actually the perceiving functions because they just "see", they don't reason to reach a conclusion, as the judging functions do. This is why Pe (extroverted perceiving) people often put off making decisions and that sort of thing - they prefer to take in info concerning the external, and their Ji (introverted judging) is more of a conceptual process that things are related to when necessary.
Fe & Fi reason to make decisions, they are not emotion. They may utilize emotion as important signals (which they are), but they can choose to discard them also.
Introverted feeling reasons using criteria of value and significance based on an innate "vision" of what is ideal. This is often why it is is associated with morals, "subjective" realms like art, looking out for the individual, inner harmony, and intrapersonal knowledge - understanding yourself & your own needs.
Extroverted feeling reasons using criteria of value and significance based on external standards; what is generally accepted or concepts of good/bad which can be validated in reality. This is often why it is associated with appropriate social expressions and behavior, cultural protocol, gauging by consensus and results, group harmony, and understanding interpersonal interactions.
There is overlap between the two because of both dealing in realms of good/bad based on value & significance. However, to reiterate the above, Fi uses an internal standard; something like the theoretical models that Ti uses for logic, only it is based on what is "ideal", and this motivates the Fi-dom to work towards finding/creating this ideal in reality. Fe uses an external standard, based on what is viable and leads to results in reality, something like how Te uses externalities to measure what is correct (ie. facts), but Fe seeks to create, maintain and use social standards to promote harmonious relationships.
