Lambda Architecture : Presents holistic view of an organization’s data , from historic and real-time view.

For workload or data load processing and presentation of the big data Nathan Marz used the term Lambda Architecture (LA).
Linear Scalable : The Architecture should scale out and should take care of different types of use cases.
Fault Tolerant : It should be capable of wide range of workloads.
There are three important layers of Lambda Architecture (Batch Layer, Speed Layer, Serving Layer) and it takes care of two important principles of architecture:
Important Characteristic of Batch Layer:
1)Distributed processing system used to precompute results.
2)Accuracy achieved by processing all available data when generating views
3)Errors are fixed by recomputing the complete data set and updating existing views
4)Output stored in a read-only database and updates completely replaces existing precomputed views
e.g. Apache Hadoop, Snowflake, Redshift, Synapse ,Big Query etc.
Important Characteristic of Speed Layer:
1)Data stream processing in real-time.
2)Latency is minimized by providing real-time views.
3)Errors are not fixed to increase throughput
4)Output is stored on fast NoSQL databases
e.g. Amazon Kinesis, Apache Storm, SQLstream, Apache Samza, Apache Spark, Azure Stream Analytics etc.
Important Characteristic of Serving Layer:
1)Output from the batch and speed layers is stored in the serving layer.
2)Responds to ad-hoc queries.
e.g. Druid.
Kappa Architecture: Jay Krepps introduced this pattern for immutable data stream as primary source to mitigate the drawback of code replication in Lambda architecture.

Main Characteristics of Kappa Architecture: It is based on immutable data stream as the primary source of record rather than point-in-time representation of databases or files. This allows unit testing and revisions of streaming calculations , not supported in lambda. It eliminates the need for a batch-based ingress processing , as all data is written as events to the persisted stream. Main advantage over Lambda Architecture is that both real time and batch processing can be performed within a single technology stack.
To simply explain Kappa Architecture, you can think of Lambda Architecture with the batch processing system removed.