In the examples above, you have two different types of movement in each of the sentences.
Indeed, both of them can be translated into English as
The man goes to Paul's house.
But this sentence has a disambiguation :
- It can mean that the man is heading towards Paul's house, not necessarily intending to visit Paul or enter the house:
Мужчина идёт (по направлению) к дому Павла.
- or it can mean that the man is going to visit Paul, or to hide in the house from hail, or maybe he is Paul's neighbor. Anyway, what matters is that the man wants to enter the house, to go into it:
Мужчина идёт в дом Павла.
So, to put it simple, when we talk about movement, the preposition в followed by Accusative means into, whereas the preposition к followed by Dative means towards.
See these examples:
- to go towards one's goal: идти к своей цели
- to go to the park : идти в парк
But note that, if we mean a meeting with a particular person, the preposition к is used :
The man goes to Paul - Мужчина идёт к Павлу (в гости).
The man takes his daughter to the doctor - Мужчина ведёт дочку на приём к врачу.
The general rules of usage of those two prepositions of movement (because I just explained the usage in your particular example) are described here even with pictures. A really nice cite for learning Russian. Note that some nouns require the preposition в, some - на.