Mambots where the ancestors of current version Joomla plugins. Mambots were introduced in Mambo and offered possibilities to add plug-in logic to your site mainly for the purpose of manipulating content. As the smallest Joomla extensions, they where smaller or bigger chunks of code executed upon being triggered by specially formatted keywords/signal words inserted in the various places of a Joomla 1.0 site.
Originally they acted only on content items - and Joomla 1.0 core supported only this, but later the functionality was extended by some developers of non-core components to act in couple of other areas too, prefacing the evolutionary step included in the core of next Joomla releases. They where replaced beginning with Joomla 1.5 by plugins. Since then their scope has been stretched and extended to such an extent that to enhance the meaning of the new functionality the developers decided to change the name from mambots to plugins. Joomla! 1.5 includes legacy support for Joomla! 1.0 mambots.
BTW, the original name seemingly is created from the "Mambo Robots" expression.