Well, jeez, this page has been nothing for long enough! Time for an irrelevantly(1) class-conscious, brief rendition of the mechanisms involved.
Please see RFC 2002.
MobileIP is a system by which an IP network node may roam throughout various IP network structures and send and receive traffic normally. But fundamentally the node does have a "home", i.e. for a good portion of the time it is somewhat associated with a computer we'd typically call its Gateway.
Imagine Jeanne leaving her comfortable suburban palace to tour the grand hotels of Europe for a month. What essentially she'd do is pay a really bored, poor other-neighborhood kid (hereafter "the Other") to sit by her phone and answer rings. She would, of course check in now and again to tell the Other exactly what kind of wine, bonbons and cheese she is consuming, i.e. where Jeanne is i.e. a callback number.
For calls coming to Jeanne at home, the Other dials Jeanne's current Euro number and presses the handsets together. This is the simplest though incorrect analogy. And it doesn't show the real benefits. I have failed my readers.
So, some real taxonomy.
The mobile IP node is called the "Mobile Agent" or MA. The home "Gateway" of the Mobile Agent is the "Home Agent" or HA. The guest "Gateway" which the Mobile Agent happens to be at is the "Foreign Agent" or FA.
There are some complications. The MA can tell the HA about its new FA, or the FA's can conspire and tell the HA which FA is the new active one.
This is useful in a variety of contexts. See the various projects for better pitches, HOWTOs and everything.
(1)Of course not so irrelevant. The employment of a computer to answer the phone means we don't have to pay--or even create--the Other. Every tool can be used for good or evil, remember this as you create them.