I think that the Stone allows you to hallucinate in somewhat controllable way to help you cope with the death of a loved one.
Similar to the Mirror of Erised, the Stone shows you whoever you need/want to see by looking inside you (for something to work with) and then projecting a very convincing illusion (for all 5 senses maybe) that only you can interact with, as long as you hold it. It probably lets your subconsciousness fill in the blanks. This projections appear to be nearly as good as real to the user, but only to him/her.
In Ch34 of DH we can see the this:
“They won’t be able to see you?” asked Harry.
“We are part of you,” said Sirius. “Invisible to anyone else.”
If that’s true then you wouldn't be able to get any information from these projections that you didn't already know. This should be relatively easy to check, you could just ask the ‘spirit’ to tell you something they would knew but you possibly couldn't and then check if it’s true. But Harry didn't ask for any such confirmation, he was only looking for courage to do what had to be done. And that’s what he got.
That being said, even if the Stone can’t actually summon the spirits of the dead, it can still be used to break boredom or loneliness, as a sounding board or to help you make decisions or draw conclusions from the data you know (subconsciousnessly) but can’t process for some reason.
But, if the Stone actually allows its user to summon the spirits of the dead then it has immense strategic/tactical importance as an intelligence gathering tool [provided its user can convince the spirits to share some info, they could get advice from everyone from Merlin to Grindelwald]; but this isn’t shown in canon where it’s used only to help people cope with death of their loved ones.
Also, holding the Resurrection Stone appears to dispel any Dementor-induced depression/fear – so, this is maybe the only immediately practical effect of the Stone. [If you need to deal with Dementors for some reason but can’t cast a corporeal Patronus]