At its simplest level, yes, it's a bit of software.
But it's a bit of software that has to talk to lots of other systems - software and hardware - and needs some human interaction to play out a channel successfully.
As with many bits of TV, if you were designing it from scratch, you probably wouldn't end up with the way things are today. But it's probably easiest to explain how things were to start with: a vision mixer, a sound mixer, and a number of live and prerecorded (film, tape, etc) sources.
Then basic forms of automation came in; which would take the prepared schedule, and with a bit of tweaking by the director, would automatically select the right source on the vision mixer; press play on the tape deck at the the right time, and so on.
And then tapes were replaced by video servers - so the automation system would be able to get the right clip from the server, copy it to the right place, and turn the data file into a video stream, that then gets switched to air.
For a channel that's largely prerecorded material (the UKTV network, say), one playout director can supervise a number of channels. They need to make sure that the channels largely keep to time, and look out for things failing, and so on.
Channels with more live material - BBC One, for example - will have just one director, and an announcer too. While some parts of the day will be prerecorded material, they also have to liaise with the directors of live programmes, and try to keep the schedule largely on track if things over- or under-run.
In these cases, the automation system won't be left to its own devices, and rather than using fixed points in the schedule, they'll have a handy 'take next' button which will trigger the next event.
A well-known brand of playout system in the UK is Omnibus, which appears to have recently bought by Miranda - there's a little about it
here.
That's a basic overview of how it works - I'm sure others here will be able to expand things or answer any more questions you've got.