to make sure that you know all the most recent facts or information about a particular subject or situation:
It's important to keep abreast of the latest developments in computers.
to walk, ride etc next to each other, all facing the same way
two/three/four etc abreast (=with two, three, four etc people or vehicles next to each other)
The planes were flying four abreast.
level with someone or something or in line with them:
As the car drew abreast of him, Jack suddenly recognised the driver.