Event streams are a log of one or more "things that happen", which are usually referred to as events. Event streams are conceptually focused around events than objects or tables, which are the typical storage unit of relational databases.
Apache Kafka and Gazette are a popular open source implementations of event streams. Amazon Web Services' Kinesis and Azure Event-Hubs are proprietary hosted implementations.
The way that data is stored affects how you can work with it. Constraints and guarantees like consistency make it easier to code certain applications but harder to build other types of applications that need performance in different ways. Event streams make it easier to build applications that analyze large amounts of constantly-updated data because the events are not stored relationally.
Some applications, such as aggregating millions of sensors, or thousands of streaming cameras, constantly output large amounts of data with no breaks. It is difficult to process such large volumes of data in traditional data stores, so event streams are built off of a simpler data structure: logs.
Logs are ordered sequences of events and they typically have less constraints than a database. In event streams, logs are also immutable. They do not change once they are written. Instead, newer events are written in the sequence as state changes. The reduced constraints compared to a database and the immutability mean that logs can handle the high throughput writes needed to keep up with the constant flood of data from the source of an event stream.
What is Apache Kafka? sounds like it just focuses on Kafka but it actually covers the fundamental concepts behind event streams and how they fit into microservices architectures.
Quora has a solid answer to the question of what is an event stream?.
Summary of the Amazon Kinesis Event in the Northern Virginia (US-EAST-1) Region is specific to AWS Kinesis but it explains how Amazon uses event streams at scale to run and coordinate a significant number of their services. When their event streams service went down... it took a whole lot of other stuff down at the same time. There is also some additional analysis in this post by an independent developer.