Denial Of Service attacks are generally malicious attempts to overwhelm the system with requests (like ping replies) to such an extent that no real information can be sent. Most likely your ISP would feel they are under attack and not be happy that you initiated it, but the most immediate result you may loose connection or it may simply seem like you are hung because your computer cannot keep up with the requests. This appears to be a testing tool for stress testing web servers so they are prepared should an actual DOS attack occur. It should have no permanent effect on your modem.
Everything sent across the internet is a packet of information. A bunch of 0's and 1's which includes an IP source and destination (generally in real attacks the sender trys to mask the true source by using slave computers or open ports on servers to forward their attacks). DDOS attacks use multiple computers to remotely attack; this is one of the many things having malware on your machine can facilitate. Basically they take over your internet connection along with thousands more infected machines to inundate a server.
So anyway, every packet of information that comes to you (or that you send) is coming (going) through your ISPs servers which means that their system has to process it first. Essentially they check the destination and if it's for your neighbor they forward it to him and if it's for you they forward it to you. Now the truth is that if this is just a simple test then it's duration is not long and your ISP isn't likely to even notice it as any different from you downloading photos of the "Kardashians" but if it takes enough bandwidth that their servers can't handle the traffic then they may consider themselves to be under attack.
The most simple attack is a ping request. It is simply a request from the sender that your computer reply "yes I'm here". If they fake the return address or it's going back to slave computers then the true sender does not get your reply so he doesn't get bogged down w/ your answers but with 1000s of ping requests your end gets overwhelmed trying to reply and soon buffers are overflowing and your connection is lost or slowed to a crawl. A typical firewall also recognizes this type of request and puts senders on ignore if it detects too many at one time, but since this is a DDOS there are potentially thousands of source IPs and the firewall needs to ignore each. (PING does have a valid function so you can't just disable it completely)