They’re supposed to work as an adaptor/buffer/filter between the technical side and the non-technical stakeholders (customers, middle/upper management) and doing some level of organising.
In my 2 and a half decades of experience (a lot of it as a freelancer, so I worked in a lot of companies of all sizes in a couple of countries), most aren’t at all good at it, and very few are very good at it.
Some are so bad that they actually amplify uncertainty and disorganisation by, every time they talk to a customer or higher up, totally changing the team’s direction and priorities.
Mind you, all positions have good professionals and bad professionals, the problem with project management is that a bad professional can screw a lot of work of a lot of people, whilst the damage done by, for example, a single bad programmer, tends to be much more contained and generally mainly impacts the programer him or herself (so that person is very much incentivised to improve).
A family of software development processes for teams, which focuses on cycles of quickly building and delivering smaller blocks of program functionally (often just a single program feature - say: “search customers by last name” - or just part of a feature) to end-users so as to get quick feedback from those users of the software, which is then is use to determining what should be done for subsequent cycles.
When done properly it addresses the issues of older software development processes (such as the Waterfall process) in siuations where the users don’t really have a detailed vision of what the software needs to do for them (which are the most usual situations unless the software just helps automates their present way of doing things) or there are frequent changes of what they need the software to do for them (i.e. they already use the software but frequently need new software features or tweaks to existing features).
In my own career of over two decades I only ever seen it done properly maybe once or twice. The problem is that “doing Agile” became fashionable at a certain point maybe a decade ago and pretty much a requirement to have in one’s CV as a programmer, so you end up with lots of teams mindlessly “doing Agile” by doing some of the practices from Agile (say, the stand up meeting or paired programming) without including other practices and elements of the process (and adjusting them for their local situation) thus not achieving what that process is meant to achieve - essentially they don’t really understand it as a software development process which is more adequate for some situations and less for others and what it actually is supposed to achieve and how.
(The most frequent things not being done are those around participation of the end-users of the software in evaluating what has been done in the last cycle, determining new features and feature tweaks for the next cycle and prioritizing them. The funny bit is that these are core parts of making Agile deliver its greatest benefits as a software development process, so basically most teams aren’t doing the part of Agile that actually makes it deliver superior results to most other methods).
It doesn’t help that to really and fully get the purpose of Agile and how it achieves it, you generally need to be at the level of experience at which you’re looking at the actual process of making software (the kind of people with at least a decade of experience and titles like Software Architect) which, given how ageist a lot of the Industry is are pretty rare, so Agile is usually being done by “kids” in a monkey-sees-monkey-does way without understanding it as a process, hence why it, unsurprising, has by now gotten a bit of a bad name (as with everything, the right tool should be used for the right job).