This is a loaded word in the law, and needs to be treated with care.
In litigation, it refers to the process whereby each party tells the other in a list what documents or other relevant information they have (a statement that the “document exists or has existed”). At the same time, the party says what documents they believe they do not have to produce (eg because they are confidential or covered by legal privilege). Each party can then ask for specific documents from the lists to be produced and included in a bundle for the court. (Different rules apply to this process in family proceedings). (Another word for this is “discovery”.)
In criminal cases, there is a duty on the prosecution to provide the defence with copies or access to all material capable of undermining the prosecution case and/or assisting the defence. This is explained in more detail on the Crown Prosecution Service website.
In family cases, the word “disclosure” is often misused by non-legal professionals to mean an allegation by a person, often a child, claiming to be the victim of some form of physical or sexual abuse. There may be a well-meant bias in favour of accepting such statements at face value, even of believing them, which risks overlooking the need for any such allegation to be proved. See, for example, the judgment of MacDonald J in AS v TH (False Allegations of Abuse)  EWHC 532 (Fam);  3 FCR 327:
“ … despite the fact that the use of the term ‘disclosure’ to describe a statement or allegation of abuse made by a child has been deprecated since the Cleveland Report* due to it precluding the notion that the abuse might not have occurred (see para 12.34(1)), every professional who gave evidence in this case (except the Children’s Guardian) used the term ‘disclosure’ to describe what the children had said to them).”
*Report of the inquiry into child abuse in Cleveland 1987 (Cm 412)