Much of it has to do with the fact that the law of contracts is common law — meaning it is judge-made law, based on previous court decisions (at least in the US, UK, and most Commonwealth countries). Other judges deciding similar cases at a later time will tend to use the same interpretation as prior cases. So once a high court, or a bunch of lower courts, decide on a particular meaning for a phrase in contract law, the phrase has additional meaning from that history of interpretation.
Parties to a contract usually want certainty of meaning: if X happens, then Y. Rather than re-write it in whatever words come to mind, they tend to go and use words that have been used before, since they know how they are likely to be interpreted by a judge. There are also some concepts of law, like “implied warranty of merchantability” or “consequential damages” that you just can’t really say another way, any more than a car mechanic could come up with another way to say “brake caliper” or a doctor would come up with a simpler term for “ulnar nerve”.
As a side effect, that conservatism of language tends to hold over phrases longer in contract law than in regular spoken language, and certain phases end up having certain specific functions. So while “timing is really important” and “time is of the essence” both mean roughly similar things in regular English (although the latter sounds a bit formal and antiquated), but the latter phrase has a history of meaning that can have certain consequences if one party’s timing is late in performing the agreement.
However, it is important to note that there is a fairly significant movement at least in US attorneys to move towards plain-English drafting .
The argument in favor is that the parties to the contracts know what all the words mean, which is particularly helpful with consumer facing contracts, or between parties who are not represented by counsel. Google’s Terms of Service are a pretty good example of this type of writing. It can protect against “I didn’t know what it meant!” defenses. It also can make negotiations simpler, as the business parties to a contract may feel that they have a more thorough understanding of what the contract means, and therefore don’t have to have their attorneys as involved as they would with a full-on legalese document.
The argument against plain English drafting is that you have less of the history of law behind the language to know what the exact effects might be. This argument is stronger where both parties are represented by counsel and something complicated is happening: large corporate mergers probably should never be written in plain English because the parties have lawyers, and the lawyers need the extra precision and interpretive certainty of more “legalese” like terms.
 See, e.g., Why Bother to Write Contracts in Plain English?