Settlement refers to the completion of a transaction or payment. In transactions, the settlement date is when ownership over a security or asset is formally transferred over to the buyer, which also pays for the transaction on the same date.
The majority of transactions settle on the second business day after the date the deal was traded. This is referred to as 'T+2' (which you will often see amid the jargon). It is slightly different in the US, where the most common settlement occurs on the same day, known as 'T+1'. However, there are exceptions to these settlement rules for both countries.
In terms of law, settlement represents two disputing parties coming to an agreement about a legal case. Often, this includes the two parties resolving the case before it has gone to court, or even during the court case.