Religious people, Christians in particular often use these as some kind of 'proof' that their religion is true. They vary from using a vague description of how they found it to be true in their life, whatever that means, to describing an intense hallucinogenic experience where god actually talks to them. The latter belong in the same category as people who sincerely believe they have been abducted by aliens. These experience are wholly unverifiable and don't deserve any inherent credibility. The former carries as much water as a sieve, as it is equivalent to saying "This is true because I want it to be true."
It should be noted to Christians that personal experiences can not be used as evidence for the veracity of any religious claim for several reasons.
1) Your religion is not the only religion making claims similar to this, you will find that every single religion in the history of the world had adherents that claimed the same things that you do. Why should I believe that your experience is genuine and that theirs is not?
2) I have no way of determining whether or not you are sane or delusional, or whether your experience was reality or hallucination.
3) Even if I could verify your experience as authentic, I have no way of conclusively linking your experience to your specific religion.
4) Similar to 3, other aspects of your religion do not check out with reality, so am I supposed to believe you based on something only you experienced?