It is simply a collection or set with operators defined on them. Nothing more, nothing less.
If the structure, with one operator, satisfies the requirements of closure, associativity, identity and invertibility in respect of that one operator, then it is a Group.
A second operator and additional qualities need to be met for it to be a Ring and further conditions are required for a Field.
If you wish to explore the basics, you can look at Group, Ring or Field in Wikipedia but make sure you also put mathematics in your search engine!
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It is usually called a set.
expression
A mathematical phrase that contains operations, numbers, or variables is called an algebraic expression. Algebraic expressions consist of constants (numbers), variables (letters representing unknown quantities), and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. These expressions can be simplified, evaluated, or manipulated using algebraic rules and properties.
A mathematical sentence that contains an equal sign is called an equation
A mathematical statement that contains an equal sign is called an equation.