In a parliamentary system, advice is a formal and usually binding instruction given by one constitutional officer of state to another.
Nevertheless, the convention that the head of state accept ministerial advice is so strong that in ordinary circumstances, refusal to do so would almost certainly provoke a constitutional crisis.
For example, many heads of state may choose not to follow advice on a dissolution of parliament where the government has lost the confidence of that body.
In some cases, whether the advice is mandatory or truly just advisory depends on the context and authority of the person offering it.
However, if a taoiseach has (in the words of the Constitution of Ireland) "ceased to retain the support of a majority in Dáil Éireann" (i.e., lost the confidence of parliament) the president has the option of refusing to follow that advice, and thus force the taoiseach to resign.