mostly used in work , when a task must be done , so you ask someone to "follow it" to check it from time to time with the person who is responsible of doing that task or work , to make sure that he is doing it and doing it right .

This is pretty common in corporate / business language. It means that you will check back later with more in formation or to see what the progress is. For example, "I will follow up with some questions after I have read the report." or "Did you follow up with Mark? He said he had some updated numbers for you." It basically means to contact someone or start a conversation with someone with the purpose of checking on any new information.

Thank you, Ian!