1. write down a statement or piece of information
take down notes
If you are watching something or listening to somebody speak and wish to make a record of it to refer back to later, you 'take it down.' In other words, you transcribe it. This expression is commonly used in both a social and professional context, and is similar to the phrase 'make a note of it.' A noun or pronoun can be used between 'take' and 'down.'
2. remove something that had previously been put up or put in place
take down a banner
This expression is usually used in reference to the removal something that has been hanging up, or the dismantling of an object or structure. It is more common in a social context. A noun or pronoun can be used between 'take' and 'down.' The phrasal verb 'bring down' has a similar meaning.