Mongodb – Mongo db and sharding / replica sets concept questions

A Replica-Set means that you have multiple instances of MongoDB which each mirror all the data of each other. A replica-set consists of one Master (also called "Primary") and one or more Slaves (aka Secondary). Read-operations can be served by any slave, so you can increase read-performance by adding more slaves to the replica-set (provided that your client application is capable to actually use different set-members). But write-operations always take place on the master of the replica-set and are then propagated to the slaves, so writes won't get faster when you add more slaves.

Replica-sets also offer fault-tolerance. When one of the members of the replica-set goes down, the others take over. When the master goes down, the slaves will elect a new master. For that reason it is suggested for productive deployment to always use MongoDB as a replica-set of at least three servers, two of them holding data (the third one is a data-less "arbiter" which is required for determining a new master when one of the slaves goes down).

A Sharded Cluster means that each shard of the cluster (which can also be a replica-set) takes care of a part of the data. Each request, both reads and writes, is served by the cluster where the data resides. This means that both read- and write performance can be increased by adding more shards to a cluster. Which document resides on which shard is determined by the shard key of each collection. It should be chosen in a way that the data can be evenly distributed on all clusters and so that it is clear for the most common queries where the shard-key resides (example: when you frequently query by user_name, your shard-key should include the field user_name so each query can be delegated to only the one shard which has that document).

The drawback is that the fault-tolerance suffers. When one shard of the cluster goes down, any data on it is inaccessible. For that reason each member of the cluster should also be a replica-set. This is not required. When you don't care about high-availability, a shard can also be a single mongod instance without replication. But for production-use you should always use replication.

So what does that mean for your example?

                            Sharded Cluster             
             /                    |                    \
      Shard A                  Shard B                  Shard C
        / \                      / \                      / \
+-------+ +---------+    +-------+ +---------+    +-------+ +---------+
|Primary| |Secondary|    |Primary| |Secondary|    |Primary| |Secondary|
|  25GB |=| 25GB    |    | 25 GB |=| 25 GB   |    | 25GB  |=| 25GB    |   
+-------+ +---------+    +-------+ +---------+    +-------+ +---------+

When you want to split your data of 75GB into 3 shards of 25GB each, you need at least 6 database servers organized in three replica-sets. Each replica-set consists of two servers who have the same 25GB of data.

You also need servers for the arbiters of the three replica-sets as well as the mongos router and the config server for the cluster. The arbiters are very lightweight and are only needed when a replica-set member goes down, so they can usually share the same hardware with something else. But Mongos router and config-server should be redundant and on their own servers.

Inserts need to be done via the mongos for splits to happen automatically. In fact, all work should be done via the mongos, not directly to the primary on one of the sets. That is why you have not seen any splits happen and your chunks are all still in one place. In terms of details, I've written up some of the details about how splits happen in a previous answer.

Note that you can split manually via the mongos if you want to, you do not have to wait for the automatic splitting to happen.