Why did the cows break into the storeshed?

This whole episode sums up the plight of the farm animals before the revolution. They are hungry and haven't been fed for days. Mr. Jones, as usual, has neglected his duties as a farmer. He spends practically the whole time getting drunk and feeling sorry for himself instead of feeding the animals like he's supposed to. And so the cows, driven by desperation, have no choice but to break into the cowshed to fill their empty bellies.
As with Animal Farm in general, this episode is an allegory for the Russian Revolution. The urban masses, driven on by hunger, staged a rebellion against the Tsarist regime in the then Russian capital, Petrograd. This led to the Tsar's abdication and the subsequent establishment of a liberal democratic government during what became known as the February Revolution.
The irony of the cows' situation is that they, and the other animals on the farm, will later experience much worse hunger when the so-called Animalist regime, under Napoleon, has been established. This parallels what happened to millions of Russian workers after the Bolshevik coup in October 1917, when hunger and repression became the order of the day in what was supposed to be a workers' state.

In chapter two of the novella, the animals rebel against Mr. Jones after he neglects to feed them for several days. Mr. Jones had recently lost a lawsuit and became extremely depressed and disheartened. He began spending the majority of his days drinking in his Windsor chair instead of taking care of the animals and his farm. Orwell writes that Mr. Jones's men were dishonest and idle and that the animals on the farm were underfed.
On the Saturday of Midsummer's Eve, Mr. Jones went into Willingdon and got so drunk at the Red Lion that he did not return home until midday on Sunday. When Mr. Jones returned home, he went immediately to bed without feeding the animals. At this point, the animals had gone multiple days without being fed, and the cows took it upon themselves to break into the storage shed to eat. Essentially, the cows broke into the storage shed to eat from the bins because they had not been fed by Mr. Jones or his men in two days.