Outreach is simply the process of reaching out to companies, organizations, communities, or individuals with the intention of building a relationship that is mutually beneficial and educational. Often, outreach entails providing services to a population that didn't know about or have access to a service before. In the business world, outreach is a primary way to raise awareness of the services and/or products of an entity and engage with populations to see if the beneficience is needed.
The primary difference between outreach and public relations is that outreach doesn't require expertise, but it requires passion and motivation to fill the gaps in the services provided by mainstream services. Public relations efforts often start with the premise that you're an expert in a specific service or product, and you want the population to see your offerings as essential.
An example of this is when a nonprofit startup plans to enter a new market in the developing world. If you're the co-founder, and you wanted to bring the idea of an education incubator to a foreign country that has never seen one, you would most likely start with reaching out to the communities and government about what the needs are and what benefit you want to bring to them.
In some aspects, outreach can lead to getting press coverage because by reaching out to a population in need with the intent of building a relationship and filling in services, your organization or company can gain traction with a broad audience through reporters and PR firms that write about your group.