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.