Astral projection is the ability to travel to places only with your
consciousness and awareness. Yogis were able to achieve this ability by
reaching one of the slowest frequency of their mind through meditation
(the point between awake and asleep. In psychology known as Theta
brainwaves). This ability can be very useful in many ways.
First, an industrial-military use of such a mental projection would be spying. To travel with just your mind to any place to retrieve information would be a huge benefit to a major corporation or a super power in developing strategy and responses to alleged threats.
Second, in a personal way, projections to spy on personal relationships would be both useful and creepy. If a person can mentally project his conscious into a private conversation with their significant other to glean information, feelings, thoughts (or infidelity), that could cause significant changes in the relationship.
Third, the ability to know people's future actions could change the future. If one spies on Wall Street traders to get inside information, one could become extremely wealthy with no visible paper trail on mergers, acquisitions, or undisclosed information that could drastically affect stock prices.
This psychic ability seems more probable to Desmond's ability than the explanation of "mental time travel." Desmond's premonitions were mostly wrong. For example, he saw Claire being rescued by helicopter, which never happened. One thinks that there were some intervening events (such as saving Charlie) which changed those visions, but we can't be sure.
The ability to astral project into another's emotions and thoughts could be in play after Desmond was supercharged with island electromagnetic energy. With this new found power would come some confusion on how Desmond would read those emotions and thoughts. This also comes to explain why the smoke monster, or Man in Black, can re-create a human being's life and project things from their past on the island: the ability access conscious, emotions and memories of human beings.
Widmore may have tapped into this psychic ability while on the island to amass his large fortune. It was the ability to see into his competitors and crush any competition was the driving force for his return to the island. Likewise, Eloise had some psychic ability to foretell Desmond's future, as well as the Oceanic 6.
If one can tap into the mind of another person to read it, one can also project the ability to tap into another person's mind and "reprogram it." We do it all the time in real life. In new relationships, we tend to go slow, get to know a person, gain their trust, capture their feelings in order to bond with them. With mental projection, it could be possible to avoid the hard work of interpersonal communications and just get to the end emotional bond attachment to you. This could explain the 180 degree emotional turns in relationship status during the island events, as the main characters feelings towards their closest friends would shift dramatically and without warning (the prime example was Kate's love interests).
If the main characters were manipulated by the island, the Others or Jacob and the smoke monsters, does that answer the big mysteries of the show? Not really. In the themes of free will vs. fate, the concept of mental manipulation is non-existent.