The idea that there could be more spatial dimensions than you can see,
was formally developed by nineteenth century mathematicians (e.g. Riemann).
Throughout the 20th century, physicists played with the idea,
but experimental evidence was remote, at best.
Until Fermilab's announcement in 2007:
evidence like that, might be called consistent with,
but was deemed statistically "insignificant"
(i.e. not compelling, given the slight imprecisions of distance measurements, etc.).

In September 2011, however, CERN confirmed the Fermilab results,
with a totally different setup, at a statistical significance of 6 sigma.
5 sigma is the usual standard for discovery announcements
when it comes to a hitherto unseen, but theoretically expected, subatomic particle.
This, however, is in the category of what (18th century mathematician) Laplace called:

The weight of evidence for an extraordinary claim must be proportioned to its strangeness
(later popularized by Carl Sagan),

so there is now a scramble to either find fault with the experimental procedure,
or further confirm the results.

What, exactly, is it they've discovered?

They've discovered that artificially generated neutrinos can cross a distance of over 700km
at a speed slightly —only slightly— in excess of Einstein's universal speed limit, symbolized c,
    as in  E = mc²

That speed limit comes with a lot of weirdness. For example:
I swear that you are aging more slowly than I am, but,
from your point of view, it's the other way around(!),
yet both interpretations can be accepted as physically true,
and there is a mathematical framework,
known as Einstein's "special" (as opposed to "general") relativity,
that prescribes exactly how to translate from one observer's point of view to another's.

Said prescription might have seemed highly speculative in 1905,
but it has been so thoroughly confirmed, on a daily basis
—and every time you start your car—
that it's really out-on-a-limb for a professional physicist to justify
the possibility of a particle traveling faster than c (the speed of light in vacuum).

The most theoretically acceptable justification these days would be,
that the particles are not, really, traveling faster than light;
rather, they are finding a spatial shortcut across dimensions unseen by us
(dimensions through which light, emitted in our awareness, does not travel).

Are we on the brink of inventing a means to send human explorers to places
many light-years away, and back, in less than one human lifetime?
No, but my inner skeptic has granted me the artistic license to speculate that,
some time in our future, a reckless and well-connected whiz-kid is able,
on the sly, to go visit Pegicornitaurs!

Back to my drawing board, for *ttobserve.