Well, there are a few factors that control the DOF.
Your HS10's sensor is smaller than D90's. Check out these sensor sizes. Sensor size in HS10 is 1/2.3" (about 6 x 5 mm), while D90's sensor is APS-C size (23.6 x 15.7 mm) - it has more than ten times the area of the HS10.
Okay, so it's bigger, why should you care? Well, if you attach the same lens to a smaller sensor, this sensor will collect a smaller portion of the image (like if you do a crop of the original image). And if you think about it, this means that it will be more zoomed in (yeah, think about it for a sec).
So: smaller sensor means more zoomed in picture.
Now comes the hard part: if (!) you could use the same lens on both sensors, you would have to zoom out on your smaller sensor to get the same picture. And less zoom means more DOF (less blur of the background) - we'll get to that later. So your HS10 will have more DOF for the same picture composition.
But you don't believe me, do you? You'll say that you have the same zoom (say 150 mm) on both cameras, right? Yeah, but that's because 150 mm on your camera is not the same as 150 mm on D90. Why not? I'll try to explain.
Like we said before, smaller sensor means more zoomed in picture. But when the photographers talk to each other, they want to say: "just put your camera to 120 mm" and they want it to mean the same no mather the sensor size. Otherwise they would first ask you for your sensor size, then compute the real mm length ;).
So camera and lens makers now show the focal distance in relative terms of 35 mm equivalent focal length. Read about it here.
More expensive cameras have a smaller DOF (greater blur) because of (amongst other things) bigger sensors.
A bigger aperture has a shallower DOF. A bigger f number (f/5.6) is actually a smaller opening than a smaller f number (f/2.8) - see the divide sign? You actually devide the focal length by a certain number: thus a greater number, smaller aperture.
You have a lens on your HS10 that can be open up to f/2.8, if you are zoomed out. But if you zoom completely in then it can be opened to only f/5.6.
But your brother may have a lens that can be more open at the same relative focal length. You didn't mention the aperture of both shots, but if you have a more open aperture on D90 then your pictures will have a shallower DOF.
Zoom (Focal Length)
More zoom means shallower DOF. It has to do with something called Circle of Confusion. Read about it here or on Google.
But in a nutshell, a longer focal length means that the lens will bend parallel rays of light less. That means that the angle between these rays will be less than in a lens with shorter focal length: and that means (this is crucial for DOF) that if they don't meet on the same point on the sensor, they will be more far apart on the sensor - thus more DOF.