A big light source will, compared to a small one, give a softer light. Also, the light will be soft if from a close source of light, where light that comes from a source at a more remote distance is hard.
So a big light source that is placed near will be soft, and a smaller light from a distance will be harder.
The sun is small, and far away, and is therefore a hard light. A cloudy weather will soften up the light from the sun, as the surface - the layer of clouds, will spread out the light on a bigger surface, and will soften the light coming through the clouds.
The same thing happens in a soft box.
Light can be measured in temperature, named Kelvin. Here on the scale will 1700 equals to a flame from a match, up to 6500-9500 that equals an LCD or CRT screen. The temperature of natural light is about 5500 - 6000 that equals daylight and electronic flash, that is what we want in our Home Studio Setup.
A bulb like those in ordinary homes, has a colour temperature at about 2500-3000, this will cause an orange colour that will look wrong, at least in colour photos. Some say you can use it, but you will have to colour-correct all shots. Viewed in b/w it will look more natural though.
LEDs can also be used, but again, you should look for some that have the right temperature, they are to be found, look in some shops selling photo gear, and browse to find LEDs made for photography. They often sell them named as continuous lights, and those lamps are also suited for video filming.
There are many light modifiers to be found. I have described some in this book. Please take a look at the Menu. The light modifiers have their own dedicated chapters.