Redditor, thimblefullofdespair, gives a fantastic explanation about what the TPP is all about.
The Trans-Pacific Partnership is a multi-layered deal whose particulars have just been agreed upon by the twelve participating countries. Its stated purpose is to reduce tariffs - taxes on bringing your goods into a country or sending them out - and therefore encourage industry by making it cheaper for importers and exporters to conduct business between these countries. Its other stated goal is to create a set of easy rules that businesses can live by when dealing between these countries.
The TPP is far more complex than that, however. Its subtextual function is to serve as a foundation from which to spread that set of easy rules to other Asian nations, with an eye to preventing China from setting standards among these countries first.
The Obama administration is concerned that it's either "us or them" and that a Chinese-led trade agreement would set rules that American businesses would find problematic.
So what does it mean for you? Let's assume you are a citizen of one of the participating nations.
Tl;dr the TPP is out to make business between these 12 countries more fair, predictable and even. It should provide more choice in goods and services and more bang for your buck, while making labor standards improve for people outside of North America who may be operating under less protections than a Canadian or American enjoys.
However, why are people concerned about the Trans Pacific Partnership?
Tl;dr the TPP puts local industries at risk, threatens jobs, attacks your privacy, and you may be looking at paying more for important medications (either directly or through your government). It's being sold as lower prices and better standards across the board, but lower prices are meaningless by themselves - purchasing power is what you really want - and there is no guarantee that standards need to be raised instead of lowered.