As mentioned before, nuclear fission generates a pretty substantial amount of energy. And the numbers alone may convince you that fission is extremely efficient. Well, efficiency isn't the only means for debate - it also involves safety, as the process can be very dangerous.
The most common nuclear reactor is known as a critical fission reactor. Here, neutrons produced by fission of atoms (such as Uranium) are used to cause further fissions, and so it is generally self-sustaining.
One of the main reasons people are against this process is the nuclear waste. Honestly, the term "nuclear waste" sounds pretty foreboding - reactions whose dangerous byproducts stay in the Earth for millions of years? That's pretty scary. Especially considering the world's nuclear fleet generates 10,000 tons of waste each year. These wastes remain deadly to living organisms for a very long time, so treatment is necessary. Byproducts like iodine-129 last for freakishly long times - in particular, this one has a half-life of 15.7 million years. That's a lot.
Another concern is the potential for accidents, such as the infamous Chernobyl explosion. The problems with these explosions are not only the initial deaths, but the potential for cancer to afflict the exposed. Decontamination costs can also prove crippling to an economy, as Chernobyl did to the Soviet economy.
Many opponents also believe fission is excessive - Helen Caldicott, Australian physician and anti-nuclear advocate, states that nuclear reactors are just dangerous, sophisticated ways of boiling water, "...analagous to cutting a pound of butter with a chainsaw." Aside from just being a fun analogy, she makes a point that many opponents agree with, that it is too costly, excessive, and dangerous to be worth the energy output.