The data gathered consists of things happening at certain energy levels. But with the bazzillions of things happening there are lots and lots of dots on the graph showing results. There are random things going on. When a bump is seen in the graph (which can be interpreted as a particle) it could be that there just happened to be a pile up of random measurements at that point.
In many studies the chance of something being there just by random chance is calculated and if the odds against it are at least 19 to 1 then it is called "significant" and the results are considered to be correct within a reasonable probability.
However, in this case they don't begin to consider that there is a real signal there until he odds against it happening randomly are oodles of bunches to one. (Someone else can supply the actually number but it's more like millions to 1 instead of 19. ) OK I looked it up and they announce at about 3.5 million to one)
As more and more data is gathered the odds the bump occurring if there is no higgs keeps getting higher. However, even 50 million to one isn't a zero chance so as is typical in the sciences they don't say "It IS the higgs." They say instead that "The chances of seeing this if there is no Higgs is 3.5 (or more) million to one".
Of course, if they aren't writing in a science paper but just speaking as a normal, rational human being at some point you stop "waffling" and say "It's the damned Higgs!" Period. Odds of 3.5 million or more seem like a good place to bet a lot that it is the Higgs.
I remember something from some announcement day press conference when reporters asked someone from one of the teams if they had found the Higgs he gave them both answers: one as a scientist and one just as a person.
If we detected giraffes by shining 3 dim lights across the jungle at about 15 feet above the ground and 20 feet apart and measured the number of times all 3 were blocked in succession then we'd have the same problem. Tree branches sway, birds fly, dust blows and antelopes jump high as well as giraffes walking by.
At some point we'd have so many cases of 3 dims in succession we might say the odds were it was an animal at least 15 feet tall. (There could be another animal out there that is also tall but not a giraffe and that is still considered in the Higgs case too but there are good reasons not to give it as much weight just like we don't in the giraffe case)
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