Everyone else has adequately explained what is going on and why and how this structure is used, but have gotten the name wrong.
These are called Nominal Sentences:
Nominal sentence is a linguistic term that refers to a nonverbal
sentence (i.e. a sentence without a finite verb). As a nominal
sentence does not have a verbal predicate, it may contain a nominal
predicate, an adjectival predicate, an adverbial predicate or even a
The examples are in line with the ones in other answers:
Nominal sentences in English are relatively uncommon, but may be found
in non-finite embedded clauses such as the one in, "I consider John
intelligent," where to be is omitted from John to be intelligent.
They can also be found in newspaper headlines, such as "Jones Winner"
where the intended meaning is with the copular verb, "Jones is the
Other examples are proverbs ("More haste, less speed"); requests
("Scalpel!"); and statements of existence ("Fire in the hole!"), which
are often warnings.
A sentence such as "What a great day today!" is for example considered
nominal because it doesn't have a verb.