There is a scientific explanation for everything. And, boy, do they throw science around (or something that sounds like science) in The Monster That Challenged the World. Overall, this is a decent 1950's creature feature. The acting is solid and most of the cinematography is good as well. The laugh out loud moment occurs when we first glimpse the creatures that look like giant sea caterpillars. Granted, they're a tad better than some of the monsters found in Roger Corman's B-movies. However, they're not very terrifying and are guaranteed to induce rolls of laughter from modern viewers.
The setting of Monster is a California Naval base that is located on a salt water lake. The monsters in question come to life after an earthquake created a fissure bottom of the lake. Supply a little radiation and, voila, giant killer caterpillars. [The movie labels them as mollusks but they look like caterpillars to me!]
Director Arnold Laven [The Big Valley, Geronimo] keeps the action moving at a nice pace and gets good performances from all of his actors. Furthermore, the underwater film sequences are unusual for the time period and while they're not up to the amazing underwater work in Creature From the Black Lagoon (1954), they're not bad either.
There are definitely better 1950's creature features than Monster, but you could do a LOT worse. In spite of it's ridiculously overblown title, Monster is an entertaining film that, by and large, holds together pretty well.
For more info check out the film's entry in IMDB.