A Wave Burst (ウェーブバースト, weebu baasuto?), also commonly shortened to Burst (バースト, baasuto?), is the name that was given to the hazardous wave flows released as solar winds and solar flares by Ra Ciela's mother star Bezel.
Due to the dimensional distortions to which Ra Ciela was subjected to with the summoning of Nei Yuuki and Nero from their respective worlds, Bezel became unstable and turned into a red giant far before the time it was supposed to, which caused its natural radiation emissions to overpower the planet's own electromagnetic field. Therefore, whenever a solar flare or solar storm takes place, the offshoot of radiation and energy will reach Ra Ciela and cause grave damages: all living beings that get caught in the impact area of a Wave Burst will die for sure, and all structures in the area will get destroyed; given the Bursts have enough power to annihilate complete cities.
While harmful, the Bursts weren't so destructive a few years before the time the events of Ciel nosurge: Ushinawareta Hoshi e Sasagu Uta take place, but given that the dimensional distortions gained double strength after Nei Yuuki came to the Universe of EXA_PICO, their power increased by a factor of ten and their frequency also increased dramatically.
It's due to this phenomenon that Ra Ciela has become a mostly barren planet, the only exceptions to this being the Colonies and the old city: the former have their own special barriers and electromagnetic field generators to repel the Bursts, while the latter is covered by a large dome called the Anti-Wave Shell; which also makes them the only places where life can thrive now. However, the Shell has started crumbling due to constantly receiving damage from the Bursts, and it's pretty common for sections of the city they are supposed to protect to end up being crushed under the resulting debris. Likewise, once a part of the Shell has crumbled away, the area it used to protect will be destroyed when another Burst occurs.