First, we have to treat the source with healthy skepticism: Google, like most other large companies, probably wanted the UK to Remain, so they're going to release data that is intended to embarrass the Leave camp since they're bitter over their loss and want to prove that the vote was bad. An article stating that Google claims this is one of the most-asked questions is fine, but it's taken as de-facto true by the WaPo, which is improper. People tend to believe these things, but even results in peer-reviewed studies are totally and completely fabricated with surprising frequency. It certainly happens a lot with unauditable data like Google Trends.

Besides being incentivized to embarrass the British people, we also have to assume that Google is squashing various forms of the query into one block: "What is the EU?", "what is eu", "what is the e.u.?", and so on would be logical, but what about just "EU"? Is it counted? Surely many people would type that in to be directed to the official EU home page.

Second, even if it is an accurate representation of the search queries in the UK, there is not necessarily heavy correlation between people that voted and people that were asking that question. Many people who cannot or do not vote use Google, especially teenagers that are tech-literate but not yet of age to vote, and they may be seeking to be informed on the monumental decision that others in the UK just made.

Third, asking Google a question doesn't necessarily mean you don't know the answer. I often conduct queries for things I already know because I want to find a citation for a specific claim, I want to find a related image, or I want to see what other people think and/or say about the thing. This is pretty typical. For example, my last search was "howard dean yell" to find a link to the clip of Howard Dean's infamous "yeah". I've known about Howard Dean's yell since it happened in 2004. That I searched for this doesn't mean that I was ignorant previously; it just means I was trying to find something concrete.

Fourth, the way that Google presents suggested questions can cause people to click the option out of convenience, curiosity, or even just proximity, so we need not assume that every query is sincere or even intentional.

So, an unbiased first paragraph of the article would be something like this:

American web search company Google has stated that the query "What is the EU?" was among the most searched today, hours after the UK voted to leave the European Union.

Compare to the actual first paragraph, which literally says "it seems many Britons may not even know what they had actually voted for." That's open hostility and bias.

Aside from all this, there is bias merely in the selection of what to publish, even if the article and headline are written in a seemingly-neutral way. The fact that WaPo is choosing to publicize Google's unverifiable declaration in the first place lets you know where they stand.