What does ´´peşinden´´ mean?And where can I use it?

after, following

e.g. Ayşe yürüyordu, Mehmet de gizlice peşinden gidiyordu. 

Ay şe was walking and Mehmet was going after (walking behind) her secretly.

Yağmurun peşinden gökkuşağı çıktı. Rainbow appeared after rain.

etc