Most words in Greek are inflected, i.e. they change their endings depending on several variables.  Inflection includes conjugation  and declension. Verbs are conjugated by changing their endings, in a conventional sequence, to indicate person, number, tense, mood, etc.  Nouns, adjectives, pronouns, etc., are declined.  Declining means "running" them through the endings that indicate their cases.  From Lesson 1, starting with the Nominative, we arrived gradually at the complete roster of cases (the complete "declension") of nouns such as  πόνος or   διδάσκαλος.

The term "conjugation" means two things: 

a) the act of inflecting verbs.  You have learned how to conjugate a few verbs.

b) a "conjugation" is also a group of verbs of a similar type that behave in identical or at least very similar ways.  In this sense, conjugations may be compared to storage bins. All the verbs that we will study systematically in the first two semesters belong to the same conjugation, by far the most predictable.  These verbs are known as " ω (omega) verbs" because that is the ending of the first person sg of the present indicative.

The term "declension" also means two things: 

a) the act of inflecting nouns, adjectives, pronouns, etc., as described above.  You are learning how to decline one type of nouns.
b) a "declension" is also a group of words of a similar type that behave in identical or at least very similar ways.  In this sense, declensions too may be compared to storage bins.

There are THREE DECLENSIONS in Greek.  Our nouns belong to the SECOND DECLENSION.  How do we know?  Thus:

Greek nouns are cited in the dictionary or a vocabulary by listing two cases: NOMINATIVE and GENITIVE.  If the Genitive of a noun ends in - ou, it belongs to the Second Declension.  Examples are:

ὁ λόγ-ος, λόγ-ου

ὁ σῖτ-ος, σίτ-ου

All the nouns we have used so far belong to the SECOND DECLENSION.  They are all masculine, and with only a few exceptions, that is the gender of nouns that end in  -ος in the Nominative and  -ου in the Genitive.  (As you know, nouns have a permanent gender, while adjectives need to shift from gender to gender in order to agree with the nouns they modify.)

But in the second declension there is another subgroup.  These are neuter.  They can be recognized because, while their Genitive ends in  -ου (otherwise they would not belong to the second declension), their Nominative ending is  -ον.  If the article is given, it is the neuter form of the article,  τό Examples of the citation of neuter nouns of the SECOND DECLENSION are:

τὸ δῶρ-ον, δώρ-ου = gift

τὸ  ἱερ-όν,  ἱερ-οῦ = temple

SUMMING UP:

If the Genitive of a noun ends in -ου, this noun belongs to the Second Declension.

If its Nominative ends in -ος, it is masculine (we do not consider exceptions yet); if it ends in -ον , it is neuter.

EXAMPLE: I decline below the neuter noun  τὸ δῶρον, δώρου.  Here is a challenge: compare its declension with that of  ὁ λόγος, λόγου and list the ways in which  the neuter noun differs.
 
 

If you identified the following peculiarities of the neuter, your answer is correct.
a) The Nominative Singular ends in -ον.
b) The Nominative Plural ends in short -α
c) Both in Singular and Plural, NOMINATIVE = ACCUSATIVE = VOCATIVE

A piece of good news about Greek grammar: b) and c) are common traits of all Greek nouns (and even adjectives, pronouns, and the article.):
 

And a peculiarity:
 

Example:

 τὰ   τῶν θεῶν    δῶρα    χαλεπά   ἐστιν.

   S ...              gen                  ......S                   PN                 V

The gifts of the gods are harsh. 

χαλεπά is an adjective.  As you will soon learn, adjectives must agree with the nouns they modify in gender, number, and case (all their variables)  so in this sentence, where the S is a neuter plural, the predicate nominative must have the neuter plural of the adjective.  If the predicate nominative were a noun it would not be able to oblige to the same extent: it would be in the gender proper of the noun and in the number required by the sense.  For instance, "Tasks are the gift of the gods" would be in Greek: 

 τὰ ἔργα  δῶρον  τῶν θεῶν   ἐστιν.

             S                 PN                 gen                      V

The subject is plural but the noun in the predicate nominative is singular.