How can an egg get tuck in the fallopian tube?

Many ways. If the tube is blocked or partially blocked, an egg can 'snag.' if the tube is open but doesn't move properly the egg/embryo can GT stuck. Some believe, and it's likely true, that an abnormal embryo may sometimes stick in a tube for reasons unrelated to the tube.
Happens all the time. Eggs are picked up by the fallopian tube and if not fertilized melt away. A fertilized egg, or embryo, can get caught in a blind cul de sac in the fallopian tube, possibly resulting in an ectopic, or tubal pregnancy.