Dear Junior
For quite some time there have been a debate on "what story points really are". To some extent there have been insightful discussions about important things to consider when sizing stories. However, the "really are" part of the debate just leaves me tired.
To discuss the true nature of story points is pretty pointless: they are a construct, created by us, and can be given any arbitrary meaning. It does not matter. What matters is whether that construct is useful for a purpose. This is the core of pragmatism.
In other words, the relevant question is not "what story points are", but "what story points are useful for". Please excuse the pun, but rephrased "What is the point of story points?"
If I try to pry things apart I can distinguish four different situations where I have found story points useful. Basically they cover the questions "Is it small enough?", "What does it cost?", "Which should we do first?", and "When can I have it?".
Small Enough
One of the cardinal faults a team can do is to start working on a story that is way to big. If they do, they will surely fail to finish it within the sprint, and having a demo with nothing to show is pretty depressing. Having a lot of half-finished work also tie their hands of what they can do next sprint. No good.
A mature team might have developed a gut feeling of how big a bite they can take and still eat it. The stories considered too big are simply sent back to product owner for delimitation or splitting.
A less mature team might see that bites have different sizes, but have not yet the insight of how big a bite they can take without choking.
Here story points can come in useful. The team can size the stories as 13, 20, 3, 8 etc. But they need not to know their limits. Instead we can observe the velocity over a few sprints and see what "small enough" means. For example, if the team have a velocity of 18, I would advice to set the limit to 9 (half velocity). So, the stories sized 3 and 8 are small enough, and those of 13 and 20 will need some more pre-sprint work to make them manageable.
It can be handy to reserve the top of backlog for stories that are small enough, a "backlog shortlist" of ready-to-develop stories. Or, if you prefer the kanban style to have one stage "delimit and split" followed by a "ready-to-develop" queue before pulling them into active development.
Cost
Whether we like it or not, the question about money always come up. It can be hard to just look at a requested feature and say how much it would cost to develop it. In a lot of development efforts the dominating cost is the cost of labour. Either the work will tax the amount of available work by the employees, or there will be contractor bills to be paid.
Here story points can come in useful. Someone probably knows what the team costs per week, or can calculate it. If you have some historical velocity data you can make a rough estimate of what each point costs. So, if you know roughly the size of the story, you can calculate the cost.
Say that your team costs EUR 27 000 a week, you run two weeks sprint, and your sprint-velocity hoover around 18. Then each point costs around EUR 3 000. So, a story of size 40 will cost roughly EUR 120 000.
Well, not all of the time will be "pure development work". There will be meetings, phone calls, administration (filling out time reports) etc. But, that does not matter. Pulling through a story of size 40 will take roughly two sprints and during that time the team will cost that amount of money.
Of course, in practice you will rather want to give an interval than a precise number. The velocity might be within 17-19 (with 90% confidence) and a "40" story can be anything from 21 to 40. So the cost will rather be in the range EUR 60 000 - 130 000. Still, it will be a figure good enough for business to decide if it is remotely interesting to proceed or not.
Priorities
A misconception among business side "customers" is that they should set priorities on business value. Well, but "economics" is really about alternatives - the cost of a bar of chocolate is that you cannot get two lollipops. In the same way, for the product owner to make a wise balance between what different stakeholders want, she must be able to compare their cost.
Interesting enough, to make priorities, we do not need to know the absolute cost of each story. It is enough to know their relative cost.
Here story points can come in useful. If feature A is size 20, feature B is 8, and feature C is 13, then we know that we can swap out feature A from a release and switch in feature B and C instead. And in doing so we do not need to care about the details of how much money it is about - all we need is aid in choosing.
Planning
Business need to look ahead to synchronize different parts of their work. E g there are some benefits in having a marketing campaign at the same time as you release some new feature of your software. But, waiting for the software to be complete before ordering the marketing will obviously make you loose market-time.
Here story points come in useful. If you observe the velocity of the team over some time you can apply some not-too-advanced statistics to predict how much work will be completed at some future point of time. Of course, each such prediction will have a probability to fail, and the surer you want to be, the lower you must set the prediction.
For example, if you have observed the velocities 36, 28, 36, 38, 24, 35, 32, 35 and you have five sprints to go, you can calculate the average and predict the team will finish 165 points. However, that prediction is just a prediction - the real result will be as likely to be higher as it is to be lower. In other words, your prediction has a confidentiality of 50 % - or a 50 % risk of failing.
If you want to make a safer prediction, say taking just a 5% risk of failing, you can calculate an interval with 95% confidentiality. In this case it will be the interval 144-186. Now you can mark the backlog, colouring all stories up to 144 as green (very likely to be delivered), those from 144-186 as yellow (totally "depends-on") and those from 186 and up as red (very unlikely to be delivered).
In Summary
It is very hard to talk about the "true nature" of story points. They are abstractions that say something about development work. And, the question of "what they really are" is not a very interesting one. Working with story points is a model, and a model should not be evaluated on "how true" it is - but on how useful it is.
Story points might be useful for a team to decide whether a story is small enough to fit in a sprint, of if it should be pushed back to the product owner - if they cannot do it by gut feeling.
Story points might be useful in assessing the cost of developing a story - if it is questionable whether its value justify the cost.
Story points might be useful for setting priorities - if it is difficult balancing the stakeholder interests.
Story points might be useful for planning at release level - if the organisation need to synch the work of different departments or groups
Apart from these four points, story points might be useful in doing other useful things - if it helps the organisation to act more wisely.
It might well be that in your particular setting, none of the "ifs" apply - and in that case story points are not useful to you. And if they are not useful, they steal time and attention from other things that would serve you better - i e they are waste that should be discarded.
In the end "what story points really are" is not as interesting as "what is the point of story points".
Yours