What does the term "Tuple" Mean in Relational Databases?

Most of the answers here are on the right track. However, a row is not a tuple. Tuples* are unordered sets of known values with names. Thus, the following tuples are the same thing (I'm using an imaginary tuple syntax since a relational tuple is largely a theoretical construct):

(x=1, y=2, z=3)
(z=3, y=2, x=1)
(y=2, z=3, x=1)

...assuming of course that x, y, and z are all integers. Also note that there is no such thing as a "duplicate" tuple. Thus, not only are the above equal, they're the same thing. Lastly, tuples can only contain known values (thus, no nulls).

A row** is an ordered set of known or unknown values with names (although they may be omitted). Therefore, the following comparisons return false in SQL:

(1, 2, 3) = (3, 2, 1)
(3, 1, 2) = (2, 1, 3)

Note that there are ways to "fake it" though. For example, consider this INSERT statement:

INSERT INTO point VALUES (1, 2, 3)

Assuming that x is first, y is second, and z is third, this query may be rewritten like this:

INSERT INTO point (x, y, z) VALUES (1, 2, 3)

Or this:

INSERT INTO point (y, z, x) VALUES (2, 3, 1)

...but all we're really doing is changing the ordering rather than removing it.

And also note that there may be unknown values as well. Thus, you may have rows with unknown values:

(1, 2, NULL) = (1, 2, NULL)

...but note that this comparison will always yield UNKNOWN. After all, how can you know whether two unknown values are equal?

And lastly, rows may be duplicated. In other words, (1, 2) and (1, 2) may compare to be equal, but that doesn't necessarily mean that they're the same thing.

If this is a subject that interests you, I'd highly recommend reading SQL and Relational Theory: How to Write Accurate SQL Code by CJ Date.

* Note that I'm talking about tuples as they exist in the relational model, which is a bit different from mathematics in general.

**And just in case you're wondering, just about everything in SQL is a row or table. Therefore, (1, 2) is a row, while VALUES (1, 2) is a table (with one row).

UPDATE: I've expanded a little bit on this answer in a blog post here.

It's a shortened "N-tuple" (like in quadruple, quintuple etc.)

It's a row of a rowset taken as a whole.

If you issue:

SELECT  col1, col2
FROM    mytable

, whole result will be a ROWSET, and each pair of col1, col2 will be a tuple.

Some databases can work with a tuple as a whole.

Like, you can do this:

SELECT  col1, col2
FROM    mytable
WHERE   (col1, col2) =
        (
        SELECT  col3, col4
        FROM    othertable
        )

, which checks that a whole tuple from one rowset matches a whole tuple from another rowset.

In relational databases, tables are relations (in mathematical meaning). Relations are sets of tuples. Thus table row in relational database is tuple in relation.

Wiki on relations:

In mathematics (more specifically, in set theory and logic), a relation is a property that assigns truth values to combinations (k-tuples) of k individuals. Typically, the property describes a possible connection between the components of a k-tuple. For a given set of k-tuples, a truth value is assigned to each k-tuple according to whether the property does or does not hold.

Whatever its use in mathematics, a tuple in RDBMS is commonly considered to be a row in a table or result set. In an RDBMS a tuple is unordered. A tuple in an MDDBMS is the instance of data in a cell with its associated dimension instances (members).

What is the tuple in a column family data store?

tuple = 1 record; n-tuple = ordered list of 'n' records; Elmasri Navathe book (page 198 3rd edition).

record = either ordered or unordered.