The parallel verses in Matthew and Mark all have different words for the introduction to this quote, but the quote is identical, taken from the Septuagint specifically Psa 118:22. As the son of a bricklayer and house builder (mistranslated into English as a "carpenter"), Christ would have understood the meaning of this stanza. This line is prophetic, describing Christ's life as one that would have an odd angle on things, so much so that he made plays on words like this one.

The word translated as "what" means primarily "anything" or "anyone," but Jesus often uses it to start a question, so it means "who," "what," or even "why". 

The verb "is" here is the common form of "to be" in Greek. It means to have a certain characteristic or remain in a certain condition. It also equates terms or assigns characteristics. -

The word translated as "this" means "from here" or "this/that thing." This word appears after "what is written" not before.

The Greek word translated as "then" either emphasizes the truth of something ("certainly", "really") or it simply continues an existing narrative. This is the second word in the phrase.

"That is written" is the Greek verb that means "to mark", "to express by written characters", "to write a letter", "to write down [a law]", and so on.  The tense is the past perfect, "has been written" and the form is an adjective used as a noun, "that which has been written".

"Stone" is from the noun which means "a stone," but there is no article introducing it, so not "the stone." There is no article before it so "a stone".

The word translated as "that" is a demonstrative pronoun (this, that), while it often acts as a pronoun, especially a connective pronoun introducing a dependent clause, the form here clearly modifies the stone so "this stone."

The word translated as "the builders" is from a verb meaning specifically to build a house but it is used generally to mean "build" or "establish." It is in a noun form so, "the ones building." This is the subject of the sentence.

"Rejected" is from a word that means specifically "reject on scrutiny", "reject as unfit or unworthy," and "reject for want of qualifications." Referring to a stone used to build a wall, we would say "reject as unfitting."

"The same" is translated from a Greek word that means "this", "that", "the nearer." It is used as a noun that acts as the subject of the sentence.

The word translated as "is become" means "become," that is, to enter or change into a new state. In Greek, especially as used by Jesus, it is the opposite of "being," which is existence in the current state. It is in the passive form, but we usually use the word "become" like a passive verb. This Greek verb, however, works differently, as we will see later in the verse.

There is a preposition here in the Greek that means "into." With the previous verse, the sense is as we use the phrase "changes into."

"Head" is from a noun that means "head of a man or beast", "an extremity", "the top", "the capital (top) of a pillar", "the coping of a wall", "the source of a rivalry," and, metaphorically the "crowning" or "completion" of a thing.

"Corner" is from the Greek noun that means "corner", "angle", "a quarter of a compass," and "a leader of people." In Greek, another meaning for "corner" is "a leader of a people." We don't use the word "corner" similarly, but the meaning is easier to understand if you think of the corners as supporting a structure, like a pillar does. We do say a "pillar of the community" to describe a leader. In Greek, they would say "the corner of a community" in the same sense.