A segmentation fault occurs when your program tries to access a region of memory in a way that is not permitted. A bus error occurs when your program tries to access a region of memory that does not exist, or it tries to access an unaligned region. See the wiki pages for examples.
SegFualts and BusErrors are runtime errors that come from accessing memory through pointers. Java has protected you from these kinds of errors by abstracting pointers away from the programing language. The only thing in Java that is similar is an ArrayIndexOutOfBounds exception that is raised when you try to access an element that is not contained in an array. In C, buffer accesses are unchecked, so this may or may not raise a segmentation fault depending on how memory has been laid out by the compiler and OS. [Note: unchecked buffers are arguably the largest source of security bugs in C/C++.]
Consider the code:
int buff[3];
buff[3] = 8;
In Java, this would throw an ArrayIndexOutOfBounds. In C, it may or may not segfault.
If the buffer buff was placed in memory next to a memory page boundary it has a greater chance of raising a segfault. The buffer buff ends at buff[2]; or rather buff has been reserved space for 3 elements. If buff[3] (or more precisely, *(buff+3), the 4th element) was on a read only page, then the assignment will generate a segfault (but a read would not). If it was on a page marked "no access," then either an attempt to read or to write would raise an error. If it was on a page that is marked as read/write, then no fault signal will be raised and the value 8 will overwrite whatever value was previously at that location. This may be empty memory (so nothing bad will happen), another variable (the old variable contents will be lost), part of the call stack (possibly causing the program to "return" to an arbitrary location), or even a piece of instruction code. If the value 8 was inputed from the user, this bug could allow a user to execute arbitrary code within the program.
In Java, these errors are always fail-stop, so they are easier to find. In C, they may or may not be fail-stop depending on how memory is arranged, so they are harder to find.
Bonus Material: The libraries Electric Fence and Dmalloc change the way in which pages are allocated to ensure that each buffer (in the heap) ends at a page boundary and that the following page is "no access." The tool Valgrind translates and instruments code to look for similar (and more) errors, and Die Hard (acm, draft) takes a probabilistic approach for laying out memory to detect these errors.
