Planning poker is a fun and simple way to implement a Delphi process. As a Delphi method, it is useful when there is very little data and large uncertainty. This works well for the Agile world since, by definition, we have not done the work to lower the uncertainty at the point the planning poker is played.
The point of any Delphi process is to bring in as much information as you can from multiple sources in a short period of time. By forcing each participant to "disclose" their estimate at the same time, differences are disclosed and can be discussed.
Of the clients I have that use planning poker, the stakeholders don't normally get to estimate. However, when they watch, they understand better why the estimate came out the way it did rather than a dark, mysterious process.