When things happen uncontrollably, they are impossible to restrain or hold back. If you're sobbing uncontrollably during your favorite sad movie, you just can't stop the tears from flowing.
Any time you lack control over something, it happens uncontrollably, like when your best friend makes a weird snorting sound during math class and you both start giggling uncontrollably. Your tiny puppy might shake uncontrollably during a thunderstorm unless you wrap her in a blanket and soothe her. This adverb comes from uncontrollable, an adjective formed by adding the prefix un-, or "not," to controllable.