Phrases and clauses can be said to be made up of heads and dependents. The head is so to speak the 'core' of the phrase, what the phrase is about.
In a possessive phrase, like 'the king's crown', the possessed item - the crown - is the head. The possessor - the kind - is a dependent or modifier. A phrase like "the king's crown' denotes a kind of crown, not a kind of king. Therefore, one can say that 'crown' is the head of the phrase.
Possessive relationships can be marked on the dependent (the king, in this case), or on the head (the crown, in this case). English, and many other languages, are dependent-marking when it comes to possessive phrases:
-A genitive case is attached to the possessor (in the case of English, the genitive case is a clitic, but it doesn't matter.)
Many other languages are head-marking when it comes to possessive phrases:
king crown-3s.M (or something)
-A possessive suffix is attached to the dependent (possessed item), showing number, person, gender etc of the possessor.
In a clause, the verb is a head, and the various arguments are dependents.
The kind sees the queen.
-This is about a kind of seeing, therefore, 'see' is the head. How does one mark the relationship between the head (the verb) and the dependents? As with possessive clauses, this can be done on the head (verb) or dependents (arguments, noun phrases)
king-NOM see queen-ACC
-Case-markers are attached to the noun phrases, telling which one is the subject and which one is the object. In many dependent-marking languages, one can switch the order of the noun phrases, without changing the meaning, due to the case-marking:
queen-ACC see king-NOM
-This would still mean that the king sees the queen, not that the queen sees the king. To say that the queen sees the king, one has to change case-markers:
queen-NOM see king-ACC
king 3sM.NOM-3sF.ACC-see queen.
-Affixes to the verb show number, person, gender etc. of the subject and object. Many head-marking languages are very free when it comes to word-order:
king queen 3sM.NOM-3sF.ACC-see
3sM.NOM-3sF.ACC queen king
queen 3sM.NOM-3sF.ACC king
These could all mean that it is the king who sees the queen. To say that the queen sees the king, one has to change agreement affixes:
king 3sF.NOM-3sM.ACC-see queen
Apart from pure dependent-marking and pure head-marking, a language can be double-marking - marking both heads and dependents:
king-GEN head-3sM - 'the king's crown'
king.NOM 3sM.NOM-3sF.ACC queen.ACC - 'the king sees the queen'
Or a language can have no overt marking at all, relying only on context and word-order:
king crown - 'the king's crown'
king see queen - 'the king sees the queen'