The NDAA means the National Defense Authorization Act. This is a yearly law passed that approves the military spending of the US government. The NDAA is often controversial because it includes additional provisions ("riders") that extend the power of the US president (in recent years).
This act has been used in the past to approve long-term no-trial detention for enemy combatants, giving the President powers to remove habeus corpus, etc. There's a lot of reasons why each one has controversy. Generally, Republicans oppose the bill because it is extremely expensive, and Democrats because of rights restrictions, but that's an extremely general statement.
In its core, the NDAA is a defense act that provides the money for the US armed forces. It is passed and signed yearly almost by rote, and because of this assured passage, both sides use the NDAA to pass policy they want. Wikipedia has summaries of individual NDAAs that may explain each one more indepth.