In constructing the Mishkan, me’amer (gathering) involved binding sheaves together; it is the fourth of the 11 agricultural melachot. For practical purposes, me’amer involves any collecting of scattered produce. It doesn’t have to be fruit, though–anything that grows from the ground is subject to m’ameir. For example, the m’kosheish eitzim (gatherer of sticks) who desecrated Shabbos in Parshat Shelach (Number 15:32) might have been guilty of me’amer (although he might have been guilty of kotzer for breaking the sticks off of trees – see Talmud Shabbos 96b).
According to most authorities, me’amer only applies (a) to things that have not been previously gathered and (b) only in the place where the things grow and their gathering normally occurs. Therefore, if you knock the bowl of fruit off your host’s Shabbos table, it’s okay to pick up the fruit and put it back in the bowl. However, if produce scatters outside, one is rabbinically prohibited from gathering it as a weekday activity that is dangerously close to m’ameir (see Talmud Shabbos 143b).
Additionally, once produce has been processed, such as weaving wool into a garment or carving a stick into a wooden spoon, m’ameir no longer applies.