Umbrellas are normally used to modify light outputs(light modifiers) as light diffuser. The wider the umbrella in diameter, the more diffused and wider coverage it will produced.
The farther the distance from your speedlight, the wider your speedlight will produce on to the umbrella. The smaller the focal length setting, the wider your speedlight will produce on to the umbrella.
The beauty of off camera strobe lighting is having an enormous control of light for your subjects. Not all umbrellas are the same, ie white, gold and silver. Umbrellas were designed primarily for non speedlight type of flashes. They were designed for those strobelights with all type of reflectors attached to them but only a couple or maybe three designed for umbrella use.
The standard reflector is about equivalent to have and angle of about 60-80 degrees, probably about a focal length of 50mm on the flash. You can experiment and try wide, 28mm, normal,50mm and tele-100mm. The larger focal length you use the stronger your speedlight output will be.
Shooting thru the umbrella will produce harsher lights and most time its only a 1 stop different in strength. But again the wider or smaller focal length the softer. Most portraitures requires umbrella feathering, (using the outer edge of the umbrella) to light the face. Direct light is more for dramatic lighting.
Then there is the question of Umbrella height angle position as well as distance in relation to the subjects as well as single or two umbrellas. The use of reflectors come to play using only one umbrella. Hope this answer a little bit.