Hi, Router, Firewalls, Switches etc all drop packets. They say they go
into the bit bucket. What in reality is this Bit Bucket. Is it the
electrical ground or a special circuitry. Please explain in detail.

Packets are processed by software on those devices (even if very
low-level software). Each interface will have a software queue.
Packets are added to the end of the queue and removed from the front
of the queue. If a new packet comes in and there is no room in the
queue, the software doesn't add it to the queue and goes on to process
the next packet. That's it. That's the famous "bit bucket."

I am only speaking about what PHYSICALLY happens and not the logical
part. I am speaking about the BIT bucket which essentially is a
Physical layer issue as compared to PACKET queue which is essentially
a network layer representation.

There is no bit bucket.  Saying that data goes into the bit bucket is
another way of saying it disappears and is lost forever.  It's just an
expression, a joke, a figure of speech, with no physical reality.

http://www.hyperdictionary.com/computing/bit+bucket

Efn is exacly right. There is no physical bit bucket. The lowest level
way to look at it is the following: When a packet comes in, it's
stored in a RAM buffer. If it can't be moved somewhere else due to
congestion ahead, the next packet receieved will overwrite the
previous packet.

One of the semiconductor manufacturers - I think it was Signetics -
some years ago offered a component called a write-only memory, or WOM.
 One of the suggested applications was as a bit bucket.

Turned out, of course, to be an April Fool's prank, although they
spent quite a bit of money on glossy ads for it.