To burst is to break outwards due to inner pressure, or a puncture (which is why your suitcase handle is very unlikey to burst!). Footballs, car tyres, cola bottles and tomatoes can burst.
To explode is to burst very violently, or to burst because of highly inflammable chemicals. A bomb, a champagne bottle, a windscreen in a car accident can explode.
To pop is to burst in a very minor way. A child's balloon, a pod of peas or a pimple can pop.