There are many English phrases that, taken literally, don’t make much sense. These phrases are called idioms. Idioms are meant to be taken figuratively, and generally stem from literal meanings of the phrase that are either relevant in other contexts, or have been relevant in the past. Although it may be difficult for non-Americans to understand some of the more complicated idioms, many are easy to figure out.
A popular American idiom is "bent out of shape." The most common context is to tell someone not to get upset over a problem. It is the same as getting worked up, aggravated, or overly annoyed at something that usually can't be helped. For example, a person might be advised to not get all bent out of shape over a minor parking ticket. It is something that can not be changed, and therefore the person should just deal with it and move on.
Another use of the phrase is for something that is slightly off from what it should be, such as a saying that someone's plans are all bent out of shape due to unforeseen circumstances. In this situation, it means that the plans that were made are messed up. Perhaps there was a lot of traffic, or someone became ill. Whatever the reason, the person would not be able to complete their plans in the way that they originally had in mind. This use is not as common as the first, but is still used on occasion.
The phrase is also common when referring to broken or bent objects, which is where the phrase was originally used. If a nail is bent out of shape, it is useless. That is why the phrase encourages people to not get irrationally upset about small problems. It is easier to solve any issues that may come up when you have a clear head and are able to think rationally. Being upset or very emotional will make it much harder to come up with a solution. Staying calm is usually the best way to approach a predicament.
There are several idioms that are very close in meaning to this phrase. One of the most popular is to advise someone "don't have a cow," or don't get "worked up" over something. If you are very bent out of shape over what someone is doing, there is a chance that you might "jump all over them" or even "blow your top."