To explain a little further but in simple terms still..
A Dos - Denial of service attack is when you make a pc (usually a pc under your control) attack another pc using a exploit. The exploit will usually be something like sending a certain packet that causes the servers programs to get confused and push cpu up by 1-2%. This is then done on 100 on the same pc using threads and the server no longer has any free system resources to serve up new visitors.
A Ddos - Distributed denial of service attack is the same as above but you use say 10000 pcs that are under your command to achieve the above goal you do not need to find such a high level exploit to pull off a ddos attack the cpu/memory ect that is used by the server could be 0.1%... with 10000 pcs hitting them they are still going down.
It takes no skill to do the above many ddos services are available to rent by the hour if u know where to go
. This has lead to alot of idiots showing off using social media , pretending to be something they are not and taking down sites for the "lulz" then acting like they are pro hackers
.
Neopets could stop ddos easy by moving to the cloud. Most cloud systems spot and will stop ddos packets before they even get to the servers router.... Well packets that ur average neopets user can launch anyway.