IP logging is when a site keeps your IP address for longer than is required.
To explain this, imagine buying something from a mail order company. They need to know your postal address in order to send your goods to you. Once they have done this, they can either keep your address (i.e. log it) or delete it. In a similar way, when you access a website, it needs to know where to send the information (the address it sends the site to is known as your IP address). They can then either record the fact that they have sent you the website (i.e. log it), or delete the fact that you have accessed their site.
Logging IP addresses has many security & privacy concerns, including: