The final phrase is 'in the park'. Here we have three kinds of words - 'in' is a preposition (because 'in' determines the position of something). 'The' is a determiner, because it determines the noun, 'park'. Here, the preposition 'in' is the most important word, because it determines where John saw Mary (without 'in' the sentence makes no sense, while 'Mary' could be changed to 'a dog' and the sentence is still easy to understand). What we have here is a prepositional phrase (PP) composed of a preposition (PP), a determiner (D) and a noun (N):
John saw Mary in the park
NP
VP
V
N
PP
D
N
PP
In fact, when you think about it, this final phrase is really two phrases combined. 'The park' makes sense all on its own, and again it is difficult to separate these two words ('the in park'?). So we can say that there is a noun phrase (NP) inside the prepositional phrase (PP), and then all the phrases can be collected within the 'sentence' (S):
John saw Mary in the park
NP
VP
V
N
PP
D
N
NP
PP
S