Learn Russian: Это самое глубокое озеро в мире.

The word for lake, озеро, is a neuter noun. When using the superlative, both the helper word самый (the most) and the adjective глубокий (deep) must change their endings to match the neuter gender. That gives us самое глубокое.

Does самое глубокое literally mean "the most deep"?

Yes! To say "the deepest" or "the most [adjective]" in Russian, you simply take the word самый and put it right before the normal adjective. As long as both words agree with the noun they describe, you've made a superlative!

Why is "in the world" written as в мире?

Because it describes a location, which requires the prepositional case. The dictionary form of "world" is мир, and as a masculine noun ending in a consonant, it takes an -е at the end to become в мире.

There is no word for "is" in this sentence. Is it just understood?

Exactly. In the present tense, Russian almost always drops the verb "to be" (am, is, are). So, Это самое глубокое озеро literally reads as "This [is] the most deep lake."