It’s electronics vs. mechanics.
There’s a device called a shutter that sits in front of the digital SLR sensor, blocking it from light.
When you take a photo, the shutter (made up of two curtains) opens and closes.
This is different from a compact camera, where there is no shutter mechanism. In compact cameras, the sensor is electronically activated every time you take a photo.
The advantage of the mechanical solution is that it is instantaneous: you press the shutter button and the shutter snaps open.
There’s never a delay when you want to capture that photo of a lifetime.
(www.digital-slr-guide.com)

If I want to take landscape photos, I attach a wide-angle lens. If I want to photograph bugs and flowers, I use a macro lens. When I take photos of my labrador, I use a telephoto lens and can snap shots even when I’m halfway across a field.
One camera, tons of lenses.Again, it comes down to speed.
Zoom lenses in compact cameras take time to zoom in and out since the zoom is driven by a motor. You manually control the zoom of a digital SLR, and can zoom as fast or slow as you like.
(www.digital-slr-guide.com)

One clear advantage of digital SLR cameras is that they’re able to capture photos even when there’s not a lot of ambient light.
So what? Every camera can take a photo when there’s not a lot of light – just turn on the flash.
Here’s the trick: digital SLR cameras can do it without the flash.Digital SLRs are able to take photos when there’s little available light because of a feature called ISO: it makes the digital sensor more sensitive to light.
While several compact digital cameras will also let you change the ISO of the camera, there is one key difference.
As you increase the ISO (and increase the camera’s sensitivity to light) you also add grain or "noise" to the image.
The advantage of digital SLR cameras when it comes to ISO is that even at high ISO settings they produce very little noise. I can’t say the same about compact cameras.
If you really enjoy taking photos when there’s not a lot of light, the image quality of a digital SLR will exceed a compact any day of the week.
(www.digital-slr-guide.com)

This is my favorite advantage of digital SLR cameras.
I don’t like a machine to be making decisions for me. While it’s right most of the time, it isn’t right ALL of the time. The human brain will always be better at judging a scene then a camera set to automatic.
With a digital SLR, you have complete control over every photo you take, and don’t have to rely on the camera to make choices for you.
Even if you’re not ready to make the jump to a fully manual camera, don’t be frightened off.
Every digital SLR camera lets you use an automatic setting, and provides you with intermediate steps that offer increasing levels of control over your images.
(www.digital-slr-guide.com)