The SPE's are what is known as a RISC processor. They are very good ones, running on a 3.2ghz clock speed and they have 128-bit registers, they can handle data packets of 32, 64 or 128. But they are not complex enough to run an OS, or to handle multitasking. They are more like gpu's. You often see RISC processors in electronic devices like cell phones, dvd players, blu-ray players, TV converter boxes.
They wouldn't be able to run an OS by themselves - but they are excellent slaves for that purpose. The ps3 has one Power PC core, they call it the PPE, and it has one SPE that is dedicated to helping it run whatever OS it's running. Start up linux on your ps3 and look at the system monitor, and it will normally report that there's 2 processors there. Only one of them is actually in full control, though.The hypervisor is in ultimate control even under linux.
Those 2 processors, ppe and spe, under linux are powerful enough to do a lot of intensive tasks. You can use the other spe's too, but most pc applications don't bother to do that. I have used my ps3 to record video of games on my pc, though only 2d games record well, the RSX is locked.
The Cell is a brilliant design because each SPE is enough of a processor that it can be given its own particular task to work on, and it will do it regardless of what the other ones and the core are doing. Since there's 6 of them, they can run all kinds of stuff with no lag. Kind of like giving a complicated job to a team with a leader and 6 workers, as opposed to giving it to a team with 2 or 4 leaders. It works better for most stuff, as long as there's not too many threads of data.