Yeah, it helps...
What you're seeing there is 'shared traffic'. I expect they've configured their cable modems to the 10. network (I know mine does). Although 10.10.10.10 seems a little fishy.
Anyway. This isn't aimed at you. The cable network has shared segments, the same way that a hub (not a switch mind) sends data to all ports, so does the cable network.
Hence you'll see ARP requests, DHCP stuff, free-floating crud passed along to your cable modem, and you'll be able to listen in on it, should you so desire.
The way I read your dump, to answer the question is :
client2.attbi.com is sending packets from port 1789 to 10.10.10.10 on port um.. (quick lookup) 6667. The packets are Reset packets with a window (return data) size of Zero. Which is expected for Reset packets.
Basically what you're seeing is some host sending traffic to some (private, and certainly not internet routable) ip address attempting to reset a connection on ircd port - Which 'services' says is internet relay chat (I assume daemon). This may or may not actually be what the port is used for.
Anyway, as I said, this traffic isn't destined for you, but since your network card is (I think - slap me if I'm wrong) being put into promiscuous mode by tcpdump you're listening in on all the conversations that happen to pass by your cable modem.. Which, under the nature of cable modems is rather alot, and probably has nothing to do with you...