Strobe vs Speedlight
+1 to what Thanasosdk said.
Your camera shutter speed is limited by its sync speed when you use studio strobes or a regular hot-shoe flash.
The flash of light from a strobe or hot-shoe flash is typically less than 1/1000sec. in duration. The short duration of the flash is what stops movement in the studio.
In the studio since the ambient light level is typically many times less than the light level of the flash so the ambient light doesn't contribute significantly to the exposure when you use apertures like f/5.6 or higher.
When you start doing shallow depth-of-field photography in the studio and using a wide aperture the ambient light level that didn't contribute a significant amount of light at f/8 becomes significant at f/2.8 and camera shake and subject movement become problems. Many times you can do wide aperture photography in the studio with only the studio strobe's modeling lights, not flash of light at all.
Outdoors the ambient light level can be high enough to contribute a significant amount of light to the exposure. This is where you need to use a hot-shoe flash that is capable of Canon's High Speed Sync or Nikon's FP High Speed Sync so you can use a higher shutter speed to stop movement.
The problem with HSS is that a hot-shoe flash is very week compared to to a studio strobe, and when you use it in HHS mode you lose another 2 to 3 stops of power since the flash is firing at a weak power level over 1000 times a second. This means that you can only use HSS with the flash very close to the subject.
The alternative is to use a ND filter on your camera but this creates its own problem, you need a flash or studio strobe that is bright enough to compete with the ambient light. Fortunately this isn't a really big problem as long as you are using the flash or strobe as a fill light where the flash or strobe contributes less than 50% of the lighting.
Below are some good free video tutorials showing how to mix a hot-shoe flash with ambient lighting. Shallow depth-of-field isn't mentioned by Joe Brady but as Thanasosdk and I said, just stick a ND filter on your camera and then you can leave your shutter speed below the sync speed and shoot with wide apertures using mixed ambient and flash.
Joe uses a flash meter but there isn't any reason why you can't do the same thing without a flash meter. I have a flash meter now, and love it, but in the past all I did was use a white card to find the right exposure. Here is how.
Living and loving it in Bangkok, Thailand. Canon 7D - See the gear list for the rest.