The G4 is a processor platform from a joint venture between Apple, Motorola and IBM (Motorola doing most of the design and IBM doing most of the fabrication). The G4 moniker is mostly an Apple-ism, and is technical known as the MPC7xxx line. Processors using MPC7xxx designs are also used in IBM workstations under the name Power4. The G4 was the successor to the wildly popular G3 processor, also from Motorola.
Currently in the Apple Macintosh line there have been several models of the G4 chip used: 7410, 7440, 7450 and probably others. Though they vary in respects such as clock speed, process size and power usage they are otherwise, for the sake of our argument, the same microprocessor.
The G4 was first seen in a production machine in October 1999 in the first Power Macintosh G4 (code named "Yikes!") and was available in 350 and 400mHz varieties; this was, for the most part, simply a Power Macintosh G3 with a G4 CPU instead of a G3. The logic board design changed and in December of 1999 the second generation "Sawtooth" models came out in 350, 400, 450, and 500mHz speeds (also sporting AGP graphics). Next speed bumps would push it to 600, 700 and eventually to 1gHz in January of 2002 where it sits currently.
Bit-wise it is fairly standard with 32-bits internally and 64-bit externally at the data bus. This usually sits on top of a 100/133mHz system bus (older/newer); this may seem slow in comparison to the Athlon 200/266 mHz bus and the Pentium IV 400 mHz bus, but keep in mind that that the Athlon bus is a double pumped 100/133 mHz bus and the P-IV is 4 concurrent 16-bit 100 mHz busses.
Early G4s sported a transistor count of a little over 10 million (in comparison the original Athlon which held over 20 million) but it's count has increased slightly as on-chip cache sizes have grown and tweaks have been made to successive generations. This lower count lays the way for what really makes the G4 special..
The Pipeline. I can't go into too much detail about CPU pipelining(follow that link to learn more about it them you ever wanted) , but suffice it to say that the length of the pipeline is a good predictor of how fast work gets done inside of the CPU. The Pentium IV has a 20 stage pipeline, the new Athlons have a 13 stage pipeline; the G4 has a 4 or 7 stage pipeline (depending if the CPU is the older G4 or the newer G4e).
What this means in real terms is that while the Pentium IV can cram in more stuff inside itself at one time (hence it's high clock speeds), but the G4 will actually (ideally) finish working on each instruction quicker because it has a smaller number of steps to get through.
I'm glossing over many technical points here, but in the interests of brevity we'll just simply say this is why a lower clocked G4s can hold up to much high clocked Pentia and Athons in many tasks. Of course, after a while the Pentium IV's CPU speeds start to make up for its lengthy pipeline, so while megahertz may not mean everything, it still means a lot.
The other big thing in the G4 is something called Altivec, also know as is the Apple pamphlets as the Velocity Engine. Altivec is a set of very, very deep instruction registers for doing floating point vector calculations. Whereas most other comparable CPUs will use their 32- or 64-bit FPUs, the G4 can use its set of 32 128-bit Altivec registers to do floating point at quite insane speeds; that is, if the software was written to support it.
But the G4 isn't without it's downsides. The biggest problem on the technical side is that the branch prediction unit is sloppy -- though this isn't as giant a problem as it would be on the P-IV because if the CPU mispredicts it can still reload another instruction in less stages then the P-IV can. It also doesn't have the ass-loads of on chip L1 and L2 cache that most x86 chips have, which is another performance penalty. And, of course, it's expensive for what you get -- sure, it's an efficient CPU, but there comes a point when raw mHz will slowly win when given enough of a difference.
Sources include Motorolas G4 whitepapers and Ars Tecnicas CPU comparison black papers.