A foaf:currentProject relates a foaf:Person to a foaf:Document indicating some collaborative or individual undertaking. This relationship indicates that the foaf:Person has some active role in the project, such as development, coordination, or support.

When a foaf:Person is no longer involved with a project, or perhaps is inactive for some time, the relationship becomes a foaf:pastProject.

If the foaf:Person has stopped working on a project because it has been completed (successfully or otherwise), foaf:pastProject is applicable. In general, foaf:currentProject is used to indicate someone's current efforts (and implied interests, concerns etc.), while foaf:pastProject describes what they've previously been doing.

Note that this property requires further work. There has been confusion about whether it points to a thing (eg. something you've made; a homepage for a project, ie. a foaf:Document or to instances of the class foaf:Project, which might themselves have a foaf:homepage. In practice, it seems to have been used in a similar way to foaf:interest, referencing homepages of ongoing projects.