Experimental results of Higgs Boson In 2012, ATLAS and CMS posted results of the mass of the Higgs boson, $126.0 \pm 0.4$ (stat) $\pm 0.4$ (sys) $\ \mathrm{GeV}/c^2$ and $125.3 \pm 0.4$ (stat) $\pm 0.5$ (sys) $\mathrm{GeV}/c^2$. 
What do these kind of uncertainty mean? Why do they use two types of uncertainty?
 A: The 'stat' part is statistical error, so you have some number of events that form a peak, sitting on some number of events that form a smooth background. Estimating the centroid of that peak involves a statistical error.
You can get idea for how that works by randomly generating a Gaussian on top of some uniform distribution: how well do you estimate the known centroid? (It's possible the Higgs peak would be Lorentzian (Cauchy) on a smooth monotonic background, but the idea is the same).
The systematic error probably has 2 main sources:
(1) How well does the detector measure the mass (which may involve 2 main sources: measuring energy (via calorimeters) and measuring momentum (via bending in a magnetic field). Calorimeters capture electromagnetic showers and count photons. Photon may be absorbed before detection; energy may escape the calorimeter. Calibrating these effects have systematic biases.
Momentum measurement involves particle ID and tracking. Tracking involves systematic errors from wire/strip position inside the track-detector, and survey errors--as one must align the sub-detector element within the whole detector apparatus, all with respect to the beam axis. There is also magnetic field calibration and uniformity concerns.
Particle ID (e.g. Cherenkov and Transition Radiation detection) can also introduce systematic errors.
(2) Modeling the background: The Higgs mass peak sits on some smooth background that must me modeled by putting the Standard Model into a massive Monte Carlo an computing the events with no Higgs Boson.
Of course, the Standard Model deals with quarks, and the experimenter has protons (in the initial state), and pions/kaons/and so on, in the final state. It is a huge modeling effort to understand the quantitative connection between the 2--one needs nucleon structure functions/generalized Parton distributions) to understand the initial state, and hardronization models to understand the final state.
When speaking with laymen, one thing they find disappointing is that there is no single event that we can say: that is a Higgs Boson decaying. Rather we say: that is what a Higgs Boson decay looks like; now this event may be a background event that doesn't involve the Higgs at all. In fact, looking at some preliminary data:

you can say, "This event is most likely is not a Higgs Boson, but it could be. Maybe... But the Higgs is there, really."
As to why this is done--the statistical error is obviously random. The systematic error may have a random component, and it may be an overall bias for all measurements. When comparing the Higgs mass to other measured masses, that can be important information.
Also: when you are systemic error dominated, more beam-time will not improve the measurement, only a better apparatus (or Standard Model Monte Carlo) will.
