The expression, mostly used in British English, has several different meanings. When you say that a machine is out of kilter, what you mean is that it is not in proper working order. It is malfunctioning.
Example:
Our TV has been out of kilter for the past two weeks.

Other expressions which have more or less the same meaning are `on the blink' and `out of whack'.
Example:
Our old tape recorders are out of whack.

They need to be replaced. When you say that someone's opinion is `out of kilter', what you mean is that it is different from those of others.
Example:
The president's views were out of kilter with public opinion.

As for the origin, well, no one is really sure where the expression comes from.