The prefix par-, when used with verbs of movement, means a direction towards home.

pareiti - to go/walk home
parbėgti - to run home
parvažiuoti - to go (by a transport) home
parskristi - to fly home
parjoti - to ride home
parplaukti - to swim home

Aš pareinu. I walk home. I come home.
Aš pareinu namo. I walk home. I come home.
Dėstytojas parbėga į namus. The lecturer runs home.
Laivas parplaukia į Lietuvą. The ship swims home to Lithuania.
Arklys parjoja vienas. The horse rides home alone.
Paukščiai neparskrenda namo. The birds don't fly home.
Tėvas parvažiuoja! Father comes (by transport) home!

The meaning of home can be figurative, like "Laivas parplaukia į Lietuvą" where Lithuania might just be the original port of the ship.

Notice that namo and į namus are redundant if used together with par-: "aš pareinu" = "aš pareinu namo". If they are used together, it is only for emphasis.