The name “mental telepathy” is fairly self-explanatory. Basically, it stands for communication by means other that those possible through our five senses. Thus, the “mental” stands for sending and receiving messages through mind activity only, as if brain information leaves your body and enters someone else's. There are numerous theories and practical uses of telepathic methods. However, none of these has still been universally proven.
Even though we are not officially capable of communicating with each other via mind messaging, most of us have noticed strangely peculiar coincidences when we think of someone and this person calls us soon after or enters the room. Also, parents can sometimes feel something unexplainable when their children are being hurt. Nevertheless, all the previously mentioned can also be mere speculation and convenient states of affairs.
The Evidence So Far
Usually, when scientists or some other people want to prove telepathy, they use means which are more or less predictable. For example, they try to guess the card from a pack. There, you have 4 different suits to choose from, meaning that you have about 25% chance of getting it right, depending on the number of different trials for the experiment. The same goes for coin flipping, where you have 50% chance of getting the side right. All these methods can be modified in favor of the telepathy theory.
Basically, if you believe in telepathy, you are definitely want to prove it and you will, subconsciously, repeat the tests until you master them and modify them in a way which proves your point. Also, statistically, you may blame your lack of success on various factors such as concentration or environment, taking only positive results into consideration.
All in all, when you “trigger” your friends to call you through telepathy, this might happen due to the fact that they were supposed to call you anyway since you have not heard from each other. Many subconscious things go past us without us being aware. So, we might use them in order to back up our telepathic powers, also subconsciously.
Finally, in order to be scientifically proven, something needs to be capable of being completely replicated by anyone who knows the formula or is familiar with the methods. Therefore, since we still cannot make telepathy universal for all human beings, we cannot claim that it exists or that it can be proven. Some day, this may be possible. Until then, we have a lot of evidence to collect.