Definition of Candidate Key:
A candidate key is a minimal set of attributes that uniquely identifies each tuple (row) in a relation (table) of a database. It is the basis for defining the primary key of a table. In other words, a candidate key is a set of attributes that can uniquely identify a record in a table without any redundancy.

Definition of Primary Key:
A primary key is a candidate key that is selected to uniquely identify each record in a table. It is a column or a combination of columns that has a unique value for each row in the table. The primary key enforces entity integrity and ensures that no duplicate or null values are allowed.

Definition of Alternate Key:
An alternate key is another candidate key that is not selected as the primary key. It can also uniquely identify each record in a table and can be used as a primary key if desired. However, the primary key is chosen based on its significance and importance in the context of the data model.

Detailed Explanation:
Candidate Key:
- A candidate key is a minimal set of attributes that can uniquely identify each tuple in a relation.
- It must satisfy two properties: uniqueness (no two tuples should have the same combination of values) and minimality (removing any attribute from the candidate key will result in the loss of uniqueness).
- A relation can have multiple candidate keys, but only one will be chosen as the primary key.

Primary Key:
- The primary key is a candidate key that is selected as the main identifier for each record in a table.
- It uniquely identifies each row and ensures that no duplicate or null values are allowed.
- The primary key provides a way to enforce entity integrity and maintain data consistency.
- It is usually represented by a single attribute, but it can also be a combination of multiple attributes.

Alternate Key:
- An alternate key is another candidate key that is not chosen as the primary key.
- It can also uniquely identify each record in a table, but it is not considered the main identifier.
- An alternate key provides an alternative option for identifying records if needed.
- It is useful in cases where the primary key may change or when there are multiple ways to uniquely identify records.

Summary:
In summary, a candidate key is a set of attributes that can uniquely identify each tuple in a relation. The primary key is a selected candidate key that uniquely identifies each record in a table, while an alternate key is another candidate key that is not chosen as the primary key. The primary key is crucial for maintaining data integrity, while an alternate key provides an alternative option for identifying records if needed.