There are two common meanings of the term "greenhouse effect". There is a "natural" greenhouse effect that keeps the Earth's climate warm and habitable. There is also the "man-made" greenhouse effect, which is the enhancement of Earth's natural greenhouse effect by the addition of greenhouse gases from the burning of fossil fuels (mainly petroleum, coal, and natural gas).
In order to understand how the greenhouse effect operates, we need to first understand "infrared radiation". Greenhouse gases reduce the rate at which the Earth's surface loses infrared radiation to outer space. Because one way to increase the temperature of anything is to reduce its rate of energy loss to its surroundings, this makes the Earth's surface and lower atmosphere warmer than they would otherwise be.