What is the difference between primary, unique and foreign key constraints, and indexes?

Primary Key: identify uniquely every row it can not be null. it can not be a duplicate.

Foreign Key: create relationship between two tables. can be null. can be a duplicate  

Primary Key and Unique Key are Entity integrity constraints

Primary key allows each row in a table to be uniquely identified and ensures that no duplicate rows exist and no null values are entered.

Unique key constraint is used to prevent the duplication of key values within the rows of a table and allow null values. (In oracle one null is not equal to another null).

• KEY or INDEX refers to a normal non-unique index. Non-distinct values for the index are allowed, so the index may contain rows with identical values in all columns of the index. These indexes don't enforce any structure on your data so they are used only for speeding up queries.
• UNIQUE refers to an index where all rows of the index must be unique. That is, the same row may not have identical non-NULL values for all columns in this index as another row. As well as being used to speed up queries, UNIQUE indexes can be used to enforce structure on data, because the database system does not allow this distinct values rule to be broken when inserting or updating data. Your database system may allow a UNIQUE index on columns which allow NULL values, in which case two rows are allowed to be identical if they both contain a NULL value (NULL is considered not equal to itself), though this is probably undesirable depending on your application.
• PRIMARY acts exactly like a UNIQUE index, except that it is always named 'PRIMARY', and there may be only one on a table (and there should always be one; though some database systems don't enforce this). A PRIMARY index is intended as a way to uniquely identify any row in the table, so it shouldn't be used on any columns which allow NULL values. Your PRIMARY index should always be on the smallest number of columns that are sufficient to uniquely identify a row. Often, this is just one column containing a unique auto-incremented number, but if there is anything else that can uniquely identify a row, such as "countrycode" in a list of countries, you can use that instead.
• FULLTEXT indexes are different to all of the above, and their behaviour differs more between database systems. Unlike the above three, which are typically b-tree (allowing for selecting, sorting or ranges starting from left most column) or hash (allowing for selection starting from left most column), FULLTEXT indexes are only useful for full text searches done with the MATCH() / AGAINST() clause.

see Differences between INDEX, PRIMARY, UNIQUE, FULLTEXT in MySQL?

Here are some reference for you:

Primary & foreign key Constraint.

Primary Key: A primary key is a field or combination of fields that uniquely identify a record in a table, so that an individual record can be located without confusion.

Foreign Key: A foreign key (sometimes called a referencing key) is a key used to link two tables together. Typically you take the primary key field from one table and insert it into the other table where it becomes a foreign key (it remains a primary key in the original table).

Index, on the other hand, is an attribute that you can apply on some columns so that the data retrieval done on those columns can be speed up.