Mentats are most useful for characters with low Intelligence. Furthermore, they are one of the games' more valuable items yet are relatively easy to find. This makes them also useful as an easy source of money, particularly when first starting.
The +1 to Charisma can allow recruiting another companion if the new Charisma is an even number. The new member will stay even if Charisma returns to the normal score.
Mentats are roughly a little bit less common than Buffout: a bit hard to find and a tad expensive, but nowhere near as rare as Psycho. However, the overall usefulness of Mentats -- aside from being able to recruit additional friends -- is a bit dubious. Even doubling up on Mentats will only increase a few skills marginally, and is far more situational.
Their name is a reference to Frank Herbert's Dune, where, in the wake of humanity rejecting artificially intelligent computers and robots, Mentats are humans trained for computer-like mathematical and logical computations. Also of note is that the pills are colored red. Red-stained lips are a distinguishing characteristic of a Dune Mentat.
According to the Fallout demo, the Mentats were syringes. The first two Fallouts' graphic's filename SYRING2 reflect this.