The Borg are a juggernaut against which resistance is futile. In Star Trek they manifest as cybernetically enhanced humanoid drones of multiple species, organized as an interconnected collective, the decisions of which are made by a hive mind.
My Take on the Borg
The standard human intellectual capacity is probably not capable of understanding the concept of a hive mind. I assume this because to My Knowledge the human mind is not (even) capable of understanding itself. We should beware of this fact whenever we struggle to understand the hive mind or the Borg.
The Borg's vision is perfection and they pursue it by adding the biological and technological distinctiveness of other species to their own. Throughout the Star Trek universe there is a permanent inconsistency as to the motives and practice of Borg assimilation. To me this feels like a reflection of the inconsistency with which contemporary western materialistic culture considers assimilation, integration and tolerance of difference. There are cases where humans encounter Borg drones and are completely ignored. In these cases the Borg do not feel threatened and thus do not attack back. This contradicts the rather sinister motives of other scenes in which Borg drones force assimilation on individuals, a process which transforms the individuals and technology into Borg, enhancing, and simultaneously controlling, individuals by implanting or appending synthetic components. In most encounters, Borg exhibit no desire for negotiation or reason, only to assimilate. They exhibit a rapid adaptability to any situation or threat, with encounters characterized by the matter-of-fact imperative "resistance is futile". The Borg thus naturally develop into one of the greatest threats to humankind. I can see some parallels to the Open Source movement (in this case the Borg) and proprietary claims (in this case the humans). But beware that this idea ever leave this web site, people would probably crucify me for this.
Where the Borg Fail
In later scenes the homogeneous and anonymous entity of the Borg is broken by the concept of a Borg Queen and central control. From a movie maker's perspective this becomes necessary in order to be able to communicate at a level that our individualistic minds work. Unfortunately this also breaks the potential of understanding more of the collective and the hive mind.
In Star Trek, attempts to resist the Borg become one of the central themes, with many examples of successful resistance to the collective, both from existing or former drones, and assimilation targets, with at least one species being shown as having superior capabilities to the Borg (namely species 8472). It is also demonstrated that it is possible to survive assimilation (most notably Jean-Luc Picard), and that drones can escape the collective (most notably Seven of Nine), and become individuals, or exist collectively without forced assimilation of others.
What most Believe
Read the Wikipedia article on Borg for the probabilistic truth on what the Borg are.