The first baby step is interwiki links. Previously, every article in every version of Wikipedia had a long list of links to every other version of that article, maintained by a small army of flaky bots that clogged up edit histories and often stepped on each others' toes. Now, there's a single Wikidata node that has the single mapping of what article corresponds to what, reflected across all Wikipedia versions. Here's "Tokyo" now:

http://www.wikidata.org/wiki/Q1490

And here's what it replaces, repeated dozens of times in every language:

http://en.wikipedia.org/w/index.php?title=Tokyo&diff=539...

The next step will be infoboxes. Instead of every Wikipedia having a separate copy of the population of Tokyo or the GDP of Canada, updated ad hoc by different people whenever they get around to it, there will be a single place storing that data automatically reflected into all Wikipedias.

And it keeps going. Taxonomies of plants and animals change all the time, Wikidata can become their single repository. Wikivoyage currently has to store the phone numbers of each hotel separately in each language version, Wikidata will allow centralizing them. Here's the master plan: