Compared to most ways of thinking about process, the value stream concern is "how we create and deliver value" rather than "how we do things".
It seems everyone in the Agile, DevOps and Tech scene are talking about Value Streams in 2020, and for good reasons. Business and manufacturing folks have been focused on value streams for decades, but as maturity and capability evolve in tech, these areas are now combining and the best of each world is being applied everywhere.

We can debate the definition of value itself in another post, but broadly, let's say: "Measure of benefit provided for a targeted recipient", and in other words: merit, worth, usefulness.
Value streams first came about as a concept in traditional physical goods manufacturing like cars and appliances, especially during the rise of Lean manufacturing to maximize efficiency, quality and value. Because of this legacy, a lot of representations you'll find are less than helpful in the digital age, but not to worry, I'll bring you the best bits here.
In short, a value stream is a process for creating value in an organization, captured in steps and measurement data. I say 'a' process, because a business is full of value streams.
Beyond Agile and DevOps
Of course you must ask: Why do we need Value Streams when we already have Agile and DevOps? One major reason is that both have proven notoriously tricky to define and execute on consistently, but the main challenge is that they each fail to cover the true flow of work resulting in customer value. Agile is at best a set of vaguely defined guidelines, and DevOps is anything from CI/CD to blameless post mortems and everything in between. They both cover either too shallow (Agile) or too narrow (DevOps) a focus to be truly actionable by a given team that needs clarity, value, and flow to perform well.
DevOps has brought visibility into the challenges of collaboration across the full flow of activities in software product development and operation, but it focuses on just a narrow slice of the process, and so issues can hide beyond its visibility.

To illustrate this another way, many teams succeed with many of the focal practices and capabilities under the DevOps tent, yet fail to truly accelerate as an organization, because a constraint exists outside of the Dev+Ops boundary.

Because a value stream by nature covers all activities from concept to cash, it gives us a better view of reality and all the requirements for delivering value. With value stream thinking, we can begin to see our organization as a collection (and even more accurately, a network) of interconnected value streams producing work that delivers value to customers. That view allows us to always focus on what is really holding us back, and what will really drive improvement, performance, and value.

The 'stream' aspect of value streams comes from the sequential series of steps performed to create value. Each one flows into the next, and the aim is to maximize the flow of value within the stream, much like a stream of water aims to deliver water as efficiently and effectively from upstream to downstream.
A value stream represents the combination of all steps from the start of your value creation (or when the process starts costing you money) until the delivery of the end result to your customer (or when the process starts making you money). A value stream is the combination of your Value Creation and Value Delivery processes in one unified flow.
Compared to most ways of thinking about process, the value stream concern is "how we create and deliver value" rather than "how we do things".
In the context of a stream, you can follow left to right, from low to high value, where each step should be adding value. This helps focus your efforts and thinking to avoid common pitfalls such as automating everything, continuing the status quo or not knowing where to start.
Good framing of the organizational challenges in striving toward success.