In Arabic, this means "son of". It is often written as the very similar bin, due to difficulty in translating Arabic grammar into English.

This word is often encountered because Arabic names are commonly in the form of:
    "A ibn B C",
where A is the person's first name, B is their father's first name, and C the family name. Hence, "Mohammad ibn Sultan Al-Mustafa'a" would denote Mohammad, son of Sultan, of the Al-Mustafa'a family.

Chosen names in Arabic are often recycled from a fairly limited pool, making this type of construction necessary. Unfortunately, even still, many names end up being very similar, varying in only one of the three names, or sometimes with all three names the same, but just in a different order. This can make things very confusing for outsiders. Another side-effect is a tendancy to list western style names in the same fashion on many documents. In my case, for example, I was listed as "Sean ibn Alan Nichols" on some papers.

Other Arabic words defining familial relationships include Bint (daughter of), Abu (father of) and Umm (mother of).