Every topic, is a particular stream of data (similar to a table in a database). Topics, are split into partitions (as many as you like) where each message within a partition gets an incremental id, known as offset as shown below.
Partition 0:
+---+---+---+-----+
| 0 | 1 | 2 | ... |
+---+---+---+-----+
Partition 1:
+---+---+---+---+----+
| 0 | 1 | 2 | 3 | .. |
+---+---+---+---+----+
Now a Kafka cluster is composed of multiple brokers. Each broker is identified with an ID and can contain certain topic partitions.
Example of 2 topics (each having 3 and 2 partitions respectively):
Broker 1:
+-------------------+
| Topic 1 |
| Partition 0 |
| |
| |
| Topic 2 |
| Partition 1 |
+-------------------+
Broker 2:
+-------------------+
| Topic 1 |
| Partition 2 |
| |
| |
| Topic 2 |
| Partition 0 |
+-------------------+
Broker 3:
+-------------------+
| Topic 1 |
| Partition 1 |
| |
| |
| |
| |
+-------------------+
Note that data is distributed (and Broker 3 doesn't hold any data of topic 2).
Topics, should have a replication-factor > 1 (usually 2 or 3) so that when a broker is down, another one can serve the data of a topic. For instance, assume that we have a topic with 2 partitions with a replication-factor set to 2 as shown below:
Broker 1:
+-------------------+
| Topic 1 |
| Partition 0 |
| |
| |
| |
+-------------------+
Broker 2:
+-------------------+
| Topic 1 |
| Partition 0 |
| |
| |
| Topic 1 |
| Partition 1 |
+-------------------+
Broker 3:
+-------------------+
| Topic 1 |
| Partition 1 |
| |
| |
| |
+-------------------+
Now assume that Broker 2 has failed. Broker 1 and 3 can still serve the data for topic 1. So a replication-factor of 3 is always a good idea since it allows for one broker to be taken down for maintenance purposes and also for another one to be taken down unexpectedly. Therefore, Apache-Kafka offers strong durability and fault tolerance guarantees.