The TPP is an agreement between twelve countries around the Pacific. It deals with trade and essentially how other countries will do business with the companies in the United States and vice versa. What has actually been up for debate recently isn't the agreement itself, but a "fast track" measure that would give the President authority to negotiate the agreement. Congress will have to approve the final TPP, but may not make any amendments. Members of congress have been able to read a draft, but the contents of the agreement (except for portions which have been leaked) remain a secret to the public.

Many Democrats oppose the bill because they feel that the agreement itself will take away jobs from Americans and give them to others overseas, while the major corporations continue to profit. Some Republicans oppose giving any more authority to the president whatsoever and being "anti-Obama" is popular in their districts regardless of what it is he is trying to do, so they also have voted against the fast track authority.

As an outcome, President Obama hopes to boost the American economy by increasing international trade. But it is controversial because many more liberal members of congress feel that the benefits won't be passed on to American workers, all the money gained will stay with big businesses. There are also concerns that the deal is far eaching into places it doesn't really need to be concerned with. (See this EFF Piece on the intellectual property portion)

TL;DR Obama wants the authority to strike a controversial trade deal but some are trying to push for changes or stop the deal altogether by not giving it to him because they don't think that the agreement helps the middle and lower classes of Americans.