A blast usually means direct force. "The gun blasted" and "the gun exploded" means completely different people were injured, and in the second phrase it was accidental. Burst means that there's a skin, cloth or membrane holding everything in, which has ruptured. Balloons, bubbles, cushions, blisters and tummies can burst. Explode means there's an internal force or reaction (chemical, pressure, nuclear) which destroys its container, and perhaps damages the surrounding area. A bomb can explode, but not burst. Often you'll see these words used figuratively.

Hello, These three words usually mean round about the same thing. You can use the three different words in different contexts and sentences, for example; I could use the word 'Blast' in a non-formal way, 'Me and Harry had a blast at the concert yesterday.' In this context the word 'Blast' would mean the two people had a very good time at the concert. You could also use the word 'Blast' when describing a sound from maybe a weapon, 'The blast was deafening, it was really loud.' For the other words 'Burst' and 'Explode' the same method can be applied to these words too, and generally the three words have the same meaning it just depends on how strong you want to make the sentence that the words are in. I hope this helps.