The galactic barrier is, by most accounts, a negative energy field either keeping stuff inside the galaxy or outside. One "authority" referred to the barrier as "a load of peanut butter." Whether he meant that the barrier was composed of peanut butter is unclear.
The barrier was once immensely powerful, but weakened considerably over a four-year period (2265-2269). When first encountered by the starship SS Valiant in 2065, the barrier caused a person to mutate and the captain to destroy his ship, but not before leaving an engraved invitation to future star-farers to tempt fate.
Which, in fact, one named Kirk did. But he had two crew members become super powerful and while he nearly wrecked his ship, Kirk got out of the episode by killing them both. (TOS: "Όπου κανένα άτομο δεν έχει πάει πριν")