The neutral second is an interval somewhere between a whole tone and a diatonic semitone (half-step). In quarter-tones it is described as three-quarters of a step, but in 31-ET it consists of four single steps. The neutral second does not occur frequently in western music, but it is a staple of Arab music. It is usually constructed by playing with quarter tones.
The neutral second provides a way to divide the minor third, other than the combination of a whole tone and diatonic semitone. This interval occurs frequently in this function in Arab music, and is one of the building block of the scales used in this music.
In the harmonic series, there are two intervals that are described as neutral seconds, the lesser (12:11) and greater (11:10) neutral seconds. In 31-ET, the neutral second more closely matches the 12:11 ratio than the 11:10 ratio, although it falls somewhere in between them. The size of this interval in 31-ET makes it similar to the interval in quarter-tones or arab music, which also matches the lesser neutral second more closely.
The neutral second is a fairly dissonant interval, so it is usually perceived as dissonant rather than consonant and implying a root. But if heard in isolation in 31-ET, if it is to imply a root, it would imply a root a lesser undecimal tritone (11:8) below the bottom note, or a perfect fourth (4:3) above the top note. This is a strange relationship and most people will likely not hear it unless the overall harmonic context implies the same root.