A high altitude balloon filled with helium floats up into the air because helium is lighter than air. During the ascent the balloon pushes air out of the way that weighs more than the total weight of the helium and the payload together. The balloon leaves the heavier air behind its path to the stratosphere and that is the reason why the balloon is pushed up into the air. The maximum altitude one balloon can reach is, theoretically, (as long as the balloon does not burst before) the altitude where external environment’s density matches that of the balloon.
As the balloon gets higher up, the air pressure reduces so the balloon is going to try to expand to compensate it. The balloon will keep on going upwards until either one of two thing happens: 1. the balloon explodes due to the difference in pressure between the inside and the outside; 2. the balloon gets so heavy that it can’t get any higher.
Summarizing, the latex balloon is holding the helium inside during the ascent phase. Up in the stratosphere, the absence of an atmosphere means that there is no pressure pushing on the balloon. If the material is strong enough or if there is enough room for the helium to expand, the balloon will not pop. Otherwise, it will explode.
Here you can see an amazing sequence explosion of a high altitude balloon full of helium (Weight: 1600gr. – Manufacturer: Hwoyee) during one of our missions: