Here is who owns the net block:

Korea Institute of Technology (NET-KIT-NET2)
373-1 Kusong-dong, Yusong-gu305-701
KR

Netname: KIT-NET2
Netblock: 143.248.0.0 - 143.248.255.255

Coordinator:
Cheon, Sunghun (SC435-ARIN) [email protected]
+82 42 869 2412

Domain System inverse mapping provided by:

NS.KAIST.AC.KR 143.248.1.177
NS.KAIST.KR.APAN.NET 192.249.24.62

Record last updated on 02-Feb-2001.
Database last updated on 18-Feb-2002 19:56:12 EDT.

What they are looking for:
Scanning you for open ports. Or probing certain ports for trojans.

Solution:
You've already done the right thing by getting a personal firewall. Just get you a good virus scanner and a trojan scanner for some extra protection. Be sure to keep your software patches and virus dat files up to date to ensure maximum protection.