A probe is an attempt to connect to or get a response from an individual service port. A scan is a series of probes to a set of different service ports. Scans are often automated.

In and of themselves, probes and scans are harmless. On the Internet, the only way to find out whether a site offers a particular service is to probe the port. How do you know if a site has a web site if you don't have its URL? You try to go to its web site. In other words, you probed its http port.

Unfortunately, probes and scans are rarely innocent anymore. They are most likely the initial information gathering phase, looking for interesting vulnerabilities prior to a launching a hacking attempt. 1998, in particular, saw an exponential rise in scans world-wide. Automated scan tools are widespread, and coordinated efforts by groups of hackers are common.