The concept of “flight of ideas” has to do with a thought disorder, generally psychosis. It is described as a rapid succession of ideas (often fleeting, partial, etc.) in which the content changes abruptly. Generally assessed through the observation of one’s speech, which will be thematically incoherent. The words themselves may be identified, but since the associated thoughts are shifting so quickly (and have no logical connection), it won’t make any sense.
The way I try to describe this symptom is through the example of television: try to make sense out of watching a series of television shows, changed randomly every couple of seconds. You might understand the words, and even glean snippets of each individual channel, but there would be no logical sense to the process as a whole. In less severe cases, there might be irrational associations from one thought to the next (i.e. two successive thoughts based on words that rhyme), but even then the process is still well beyond coherent.
This symptom typically presents during a manic episode, and may be seen to a less significant degree in a hypomanic episode (depending on the type of Bipolar disorder an individual is experiencing). Flight of ideas may also present in individuals experiencing schizophrenia, or some other form of a psychotic break (for example, psychosis resulting from substance use).
While flight of ideas is generally assessed through an individual’s speech (and it is often obvious pretty quickly), one may also see this through the individual’s writing. As described above, one will see a document written with recognizable words (usually!), but it won’t make any sense. You may see bits of associations between the rambling thought process, but the overall theme will present as nonsensical. Often, one will also observe certain elements of delusional thinking also present in the writing, if the person is also experiencing that difficulty (for example, the names of celebrities, politicians, etc. might be included).
The presence of flight of ideas indicates a severe mental health problem, though the treatment and prognosis depends to a large degree on the cause of the thought disorder. For example, substance-induced disorganization will typically dissipate as the drug is metabolized. More significantly, a manic or schizophrenic disorganization typically requires treatment with medication.