Indeterminism should be a failure in one or more of the many determinisms.
The term is most often used in connection with causal determinism and with limits on physical or mechanical determinism.
Logical philosophers describe indeterminism as simply the contrary of determinism. If a single event is undetermined, then indeterminism would be "true", they say, determinism is false, and this would undermine the very possibility of certain knowledge. 1
Some go to the extreme of saying that indeterminism makes the state of the world totally independent of any earlier states, which is nonsense, but it shows how anxious they are about indeterminism.
The core idea of indeterminism is closely related to the idea of causality. Indeterminism for some philosophers is an event without a cause (the ancient causa sui. But we can have an adequate causality without strict determinism, the "hard" determinism which implies complete predictability of events and only one possible future. We can call this "adequate determinism."
Causality does not entail determinism
An example of an event that is not strictly caused is one that depends on chance, like the flip of a coin. If the outcome is only probable, not certain, then the event can be said to have been caused by the coin flip, but the head or tails result was not predictable. So this causality, which recognizes prior events as causes, is undetermined.
Indeterminism is also closely related to the ideas of uncertainty and indeterminacy. Uncertainty is best known from Werner Heisenberg's principle in quantum mechanics. It states that the exact position and momentum of an atomic particle can only be known within certain (sic) limits. The product of the position error and the momentum error is equal to a multiple of Planck's constant.
Indeterminism is important for the question of free will because strict determinism implies just one possible future. Indeterminism means that the future is unpredictable. Indeterminism allows alternative futures and the question becomes how the one actual present is realized from these potential alternatives.
The departure from strict causality is very slight compared to the miraculous ideas associated with the "causa sui" (self-caused cause) of the ancients.
Despite David Hume's critical attack on the necessity of causes, many philosophers embrace causality strongly. Some even connect it to the very possibility of logic and reason.
Even in a world that contains quantum uncertainty, macroscopic objects are determined to an extraordinary degree. Newton's laws of motion are deterministic enough to send men to the moon and back. Our Cogito model of the Macro Mind is large enough to ignore quantum uncertainty for the purpose of the reasoning will. The neural system is robust enough to insure that mental decisions are reliably transmitted to our limbs.
We call this determinism, limited as it is in extremely small structures, "adequate determinism." The world is adequately determined to send men to the moon. The presence of quantum uncertainty properly leads logical philosophers to call the world "indetermined." But indeterminism gives a misleading impression when most events are overwhelmingly "adequately determined."
There is no problem imagining that the three traditional mental faculties of reason - perception, conception, and comprehension - are all carried on deterministically in a physical brain where quantum events do not interfere with normal operations.
There is also no problem imagining a role for randomness in the brain in the form of quantum level noise. Noise can introduce random errors into stored memories. Noise could create random associations of ideas during memory recall. This randomness may be driven by microscopic fluctuations that are amplified to the macroscopic level.
Our Macro Mind needs the Micro Mind for the free action items and thoughts in an Agenda of alternative possibilities to be de-liberated by the will. The random Micro Mind is the "free" in free will and the source of human creativity. The adequately determined Macro Mind is the "will" in free will that de-liberates, choosing actions for which we can be morally responsible.
For Teachers
For Scholars
1. C.D.Broad, 1934 "Indeterminism, is the doctrine that some, and it may be all, events are not completely determined."
Oxford: "The view that some events have no causes." (sic), Oxford Dictionary of Philosophy, 1994, Simon Blackburn.
Oxford: Indeterminism means - "Determinism is false. Its negation is true - so long as somewhere in the universe some occurrence violates the thesis of determinism."
"an extremely strong version of indeterminism is...The world at any time and in all its aspects is totally independent of its state at any earlier time.", Oxford Companion to Philosophy, 1995, Ted Honderich.

Chapter 3.7 - The Ergod Chapter 4.2 - The History of Free Will
Part Three - Value Part Five - Problems