These are the things that do the job of the old traditional vertical sash window cords and weights.
They are in principle a spring in a tube. Specified for each individual design style and weight, they act as the name suggests, to balance the weight of the window sash, so that they are easy to lift or lower, and hold in place.
If one fails, the window sash can fall, or stick at an angle and be difficult to open or close. (You should always be careful of fingers especially, when handling sash windows. They overlap in the middle so could trap fingers, or if a balance fails, could fall onto fingers).
If a sash window is not staying where you position it, tilts and sticks at an angle, or crashes down, try to carefully close and lock it, while calling us to attend and examine it, to provide a free quotation for repair.
DO NOT INTERFERE WITH THE BALANCE TUBE OR THE FIXINGS AT ANY POINT. The spring is under tension and could fly out causing injury.