like Table 5 said it's the long exposure. If you have a standard point purchased in the last few years there's probably an "extended exposure" setting, or "starry sky" where you can set the exposure to be open 15, 30, or 60 seconds. A "night time scenery" may get you the effect you're looking for but it won't be a standard X amount of seconds of open shutter, which is what you want for your desired effect.
I love playing with the settings on my camera (Panasonic Lumix DMC-TZ3) and last summer with the 60 second exposure on "starry sky" I took this:
it's still not an SLR, and the fireworks would have turned out better on a 15 second exposure I think, regardless you get the idea.