Puddles are created when it rains. Essentially, random blocks of dirt/grassy dirt on the surface are destroyed and replaced by water source blocks. These "puddles" remain after the rain has stopped. They will theoretically not be created if Griefing (any form of block breaking other than directly by a player) is turned off. (Verification needed.)
If puddles are enabled, you need not worry about them littering your world; after it stops raining they will eventually turn back into dirt.
This effect can be removed in misc.cfg at within the biomesoplenty config file by setting B:"Enable Puddles During Rain"=true to B:"Enable Puddles During Rain"=false. This may or may not work for versions other than 22.214.171.1244 depending on if the correlating line of code is within the misc.cfg file.