Most of the games on it are family oriented or they have some educational purpose in mind. Such as the games that teach you how to speak other languages or help stimulate your mind, ie: Brain age. Granted the psp has far better graphics and awesome games, but most parents buy their childern the Ds, since it is also slightly cheaper. Also it has the touch screen which lets you interact more with the software which appeals more to some people, where the PSP uses the joystick button combo. Both are awesome systems and I'm looking into getting a PSP as well so dont take it as I'm all about the DS.
A lot of people will attest that the DS just has better games. Of course that is completely subjective, but then again so is every opinion. Don't let the fact that people may prefer a different system than you bother you.
I always thought that the DS was a great system since I got one back on Christmas 2004, and I just assumed that the PSP was an awful little system because it only has ONE analog stick and I always disliked Sony... until I got a PSP half a year ago. I feel like the past half-decade of my life would've been so much better if I got a PSP instead, it's so cool to play PS1 games on my PSP and I like UMDs(mini disks in a handheld? What a novelty). It seriously sucks that the PSP only has one analog stick but games like Resistance Retribution control faaairly well, Metal Gear Solid: Peace Walker works pretty well on the system as well. The NGP is coming out soon so I wouldn't really recommend anyone buy the PSP3000 unless they have a reaaaaally low gaming budget, though I do say that it's much better to drop $130 on a PSP than on a DS Lite/DSi/DSi XL or the disappointing 3DS. PSP all the way, I never thought I'd say this.