When a signal is looped back into the system that produced it, the resulting effect is called feedback.
Feedback can be positive or negative, but these terms do not imply whether the feedback is wanted or not.
Feedback causes the output to depend not only on the current values of the inputs but on what they were in the past, because one input is actually the prior output. This is why an electrical circuit with feedback is called a sequential electric circuit. One main element of sequential electric circuits is the flip flop.
In general, feedback is positive when the reaction of the system goes in the same direction as the initial signal. The most likely best-known example for this is audio feedback. An example of a non-technical feedback loop is the spreading of a rumor in the mass media: One person makes a plausible claim and other sources repost it, causing yet more sources to post it.
When the system reacts to a signal by going into the opposite direction, there is a negative feedback. For example, a thermostat reacts to temperature changes by countering the observed trend: When the temperature sinks under the lower border, it increases the temperature; and when the temperature is above the upper border, it reduces the temperature.
Negative feedback is an important concept in linear control systems. Often one needs to maintain a property of some apparatus at a desired value. For example, the speed of a car, the temperature of an oven, or the thickness of a wire being drawn in a factory may need to be held very constant. In such systems, the value of that property is measured continuously and compared to the desired value -- the "set point". The deviation from the set point is returned to the apparatus as negative feedback, so that the system responds in a way to reduce the deviation. A system with a very slow response, such as the steering of a ship, can be challenging because the over-correction from a too-strong feedback can lead to oscillations. Systems that are inherently unstable, such as a broomstick balanced on one's finger, are also challenging. In such systems, whether the feedback loop is closed by human or machine, it is necessary to carefully filter the signals to ensure stability.