Depending what your question really is, if you are within a module that inherits from UserModuleBase or PortalModuleBase, you can simply get call the property "this.PortalId" to get the portal id and "this.PortalAlias" to get the alias.  Otherwise, if you need to gather more information, you could call the following method(s) to get the portal info

DotNetNuke.Entities.Portals.PortalController pc = new DotNetNuke.Entities.Portals.PortalController();
DotNetNuke.Entities.Portals.PortalInfo info = pc.GetPortal(PortalId);

Hope that answers your question.

From a page you can always call:

PortalSettings settings = DotNetNuke.Entities.Portals.PortalController.GetCurrentPortalSettings();

The PortalSettings object has a "PortalId" property that you can call to find out what the portalid of the current portal instance is.  If you are trying to figure out what it does in the background, I suggest you either download the sourcecode or use Reflector to disassemble the code (http://www.aisto.com/roeder/dotnet/)

The database makes pretty heavy use of portal id to decide which "portal" the tabs belong to (so the tabs table); which portal the users belong to (Users table); which portal roles are in (Roles and RoleGroups tables); and much much more.  Essentially you could say that the entire DotNetNuke process is driven by portalid because it supports multiple child portals.  Your default portal is portal 0, of course, but again, you can have any number of child portals in addition to the parent.