Learn Russian: Это платье красивое.

Because the word for "this" has to match the gender of the noun it points to. The word for dress, платье, is a neuter noun (which you can often guess because it ends in -е). Therefore, we use the neuter form это instead of the masculine этот or feminine эта.

I've seen это used to mean "This is". Does Это платье mean "This is a dress"?

It could, but not in this sentence! When это stands alone to introduce something, it means "this is" (as in Это платье. = "This is a dress."). But here, it is grouped with the noun to point out a specific item, simply meaning "this". Because we have the descriptive word красивое at the end, Это платье acts as the subject: "This dress [is] beautiful."

Why does the word for beautiful (красивое) end in -ое?

Just like "this", adjectives (describing words) must match the gender of the noun they describe. Since платье is neuter, the adjective takes the standard neuter ending -ое. If you were describing a masculine noun, it would be красивый, and for a feminine noun, красивая.

Where is the word for "is" in this sentence?