Why and how do systems get broken into?

It could be to get your personal data, to cause damage, for braging rights, to show they can get in... or most likely simply as a means of entry into yet more systems. By hopping between many machines, crackers "launder" their connections in hope of confusing any possible pursuers. Some crackers might think that it's "really neat iner-network sightseeing" to hop over 5 machines, 2 gateways and an X.25 network just to knock on the doors of some really famous company or institution (eg: NASA, CERN, AT&T).

There are many possible ways a cracker can get into your system... For example, trojan-horses/backdoor programs can be running hidden servers on your systems without your knowledge, unpached OS might have some security holes, etc. Ignorance on your part, or other local network users' attitude towards security could also be the cause - using weak passwords, sharing passwords with others, thinking it's irrelevant what security is in place for accessing the LAN...

Learn the most common security threats, teach all users of your network about security, then when you're certain everyone fully understands, configure your system in such a way that noone (including you) can possibly get it wrong :). In other words, use all the security tools available to you.