What is Alliance?

Legal Definition
An alliance is a relationship among people, groups, or states that have joined together for mutual benefit or to achieve some common purpose, whether or not explicit agreement has been worked out among them. Members of an alliance are called allies. Alliances form in many settings, including political alliances, military alliances, and business alliances. When the term is used in the context of war or armed struggle, such associations may also be called allied powers, especially when discussing World War I or World War II.

A formal military alliance is not required for being perceived as an ally—co-belligerence, fighting alongside someone, is enough. According to this usage, allies become so not when concluding an alliance treaty but when struck by war.

When spelled with a capital "A","Allies" usually denotes the countries who fought together against the Central Powers in World War I (the Allies of World War I), or those who fought against the Axis Powers in World War II (the Allies of World War II). The term has also been used by the United States Army to describe the countries that gave assistance to the South Vietnamese during the Vietnam War.

More recently, the term "Allied forces" has also been used to describe the coalition of the Gulf War, as opposed to forces the Multi-National Forces in Iraq which are commonly referred to as "Coalition forces" or, as by the George W. Bush administration, "the coalition of the willing".

The Allies in World War I (also known as the Entente Powers) were initially the United Kingdom, France, the Russian Empire, Belgium, Serbia, Montenegro and Japan, joined later by Italy, Portugal, Romania, the United States, Greece and Brazil. Some, such as the Russian Empire, withdrew from the war before the armistice due to revolution or defeat.
-- Wikipedia
Legal Definition
Relationship. The union or connexion of two persons or families by marraiage, which is also called affinity. This is derived from the Latin preposition ad and ligare, to bind. Vide Inst 1, 10, 6; Dig 38, 10, 4, 3; and Affinity.
-- Bouviers Law Dictionary
Legal Definition
International law. A contract, treaty, or league between two sovereigns or states, made to insure their safety and common defence.

2. Alliances made for warlike purposes are divided in general into defensive and offensive; in the former the nation only engages to defend her ally in case he be attacked; in the latter she unites with him for the purpose of making an attack, or jointly waging the war against another nation. Some alliances are both offensive and defensive; and there seldom is an offensive alliance which is not also defensive. Vattel, B. 3, c. 6, 79; 2 Dall. 15.
-- Bouviers Law Dictionary
Legal Definition
The relation or union between persons or families contracted by intermarriage. In international law. A union or association of two or more states or nations, formed by league or treaty, for the joint prosecution of a war, or for their mutual assistance and protection in repelling hostile attacks. The league or treaty by which the association Is formed. The act of cohfed-erating, by league or treaty, for the purposes mentioned. If the alliance ls formed for the purpose of mutual aid in the prosecution of a war against a common enemy, it is called an "offensive" alliance. If it contemplates only the rendition of aid and protection in resisting the assault of a hostile power, it is called a "defensive" alliance. If it combines both these features, it is denominated an alliance "offensive and defensive."
-- Black's Law Dictionary