In short: A will is a document in which a person decides what should happen to their property after their death, within the limits allowed by law.
Simply put: Without a will, property is inherited under the law — by the closest relatives. With a will you can arrange things as you wish, but the form and limits are set by national law. In the EU, Regulation (EU) No 650/2012 decides which country's law applies to a cross-border inheritance; you may choose the law of your nationality.
Example: A widower with a €120,000 flat and €20,000 in savings wants the savings to go towards his granddaughter's education. He consults a notary and makes a will in the form the law requires.
Watch out: Exact rules, deadlines and fees — only from a notary or lawyer. This is a map, not legal advice.
Example: Bulgaria — A will is either handwritten or notarised (Inheritance Act). Without a will, the estate passes by law — who inherits depends on how close the relationship is (children, spouse, parents, brothers and sisters — Inheritance Act, Art. 5–9).
Check in your country — The European e-Justice Portal has a "Succession" page for every EU country.
Source: Your Europe, "Managing an inheritance" — https://europa.eu/youreurope/citizens/family/inheritances/managing-inheritance/index_en.htm · European e-Justice Portal, "Succession — Bulgaria" — https://e-justice.europa.eu/topics/family-matters-inheritance/inheritance/succession/bg_bg