Trade is not, strictly speaking, the issue. It's fairly easy to trade. If this was just about giving people in 3rd world countries access to US markets, then that would fairly easy to do. If nothing else the US has some of the highest tariff barriers in the world.
No, the issue is local law. It's very easy for governments to pass a law that makes trade vastly. The classic example was France requiring, for all wine in France, that country of origin to be labelled using a French-style label. This meant that French wine-makers could use the labels they already used, and foreign wine-makers couldn't sell their products in France unless they specifically re-labelled them for the French market.
The aim of the TTP is to make that impossible. To prevent local governments from passing regulations about what is sold in their countries, irrespective of their reasons, and to allow companies to sue governments that break this. The effect of this is to give multinational corporations, the only ones with the money to make use of lawsuit provisions, more power over national governments, particularly the national governments of less powerful countries.
Obviously this has to be done in secret, because it involves sacrificing protections that people in those various countries are quite fond of. For example, in the UK it would involve abandoning a policy of encouraging farmers in remote areas of the world to grow food or cash crops rather than drugs. This has been highly successful in reducing drug production, far more so than US 'war of drugs' operations in comparable regions. But it has to go because it's a subsidy, and thus unfair to US-based food giants. Similarly, 'product dumping' or selling goods in 3rd world countries at below the cost of production, in response to a temporary surplus or in order to grow market share, is a practice that has to be shielded against governments of those countries trying to protect local producers. Animal welfare is out, of course, as are a fair number of labelling or tracking schemes.
In other words, it's an international treaty, designed by those who support an ideology of free trade as being more important than any other consideration, that is intended to support large international companies at the expense of local producers and governments. It's intended to clear a path for international trade to dominate local trade, and to ensure that producers in large western countries can use their own local legal systems to resolve any disputes that might arise. This will lower prices, but it's far from clear if it is a good thing overall.
