There seems to be a lot of confusion about the TPE so I'm going to do my best to explain.

(h) Assigned Player Exception
(1) Subject to the rules set forth in subsection(k) below, a Team may, for a period of one year following the date of the assignment of a Player contract to another Team replace the Traded Player with one or more players acquired by the assignment as follows:
(ii) - If a team's assignment of a Traded Player and acquisition of one or more Replacement players do not occur simultaneously, then the post-assignment Salary or aggregate salaries of the Replacement Player(s) for the Salary Cap Year in which the Replacement Player(s) are acquired may not exceed 100% of the pre-assignment salary (or Base Year Compensation) of the Traded Player at the time the Traded Player's contract was assigned, plus $100 000.

Source - NBAPA Collective Bargaining Agreement: Article VII, Section 6(h)

Traded Player Exception: If a team trades away a player with a higher salary than the player they acquire in return (we'll call this initial deal "Trade #1"), they receive what is called a Traded Player Exception, also known colloquially as a "Trade Exception". Teams with a trade exception have up to a year in which they can acquire more salary in other trades (Trade #2, #3, etc) than they send away, as long as the gulf in salaries for Trade #2, #3, etc are less than or equal to the difference in salary for Trade #1. This exception is particularly useful when teams trade draft picks straight-up for a player; since draft picks have no salary value, often the only way to get salaries to match is to use a trade exception, which allows trades to be made despite unbalanced salaries. It is also useful to compensate teams for losing free agents as they can do a sign and trade of that free agent to acquire a trade exception that can be used later. Note this exception is for single player trades only, though additional cash and draft picks can be part of the trade.

Source - Wikipedia (NBA Salary Cap)

OK. So. Essentially what this TPE means for the Raptors is this:
The Raptors are perilously close to exceeding the salary cap this coming season. The greatest repercussion is that the Raptors are unable to build through trades or signings for fear of paying luxury tax. Sending Bosh to Miami through the S&T requires that Miami return salary which matches within 15% plus 100 000 dollars. This value is determined based on Bosh's Base Year Compensation on whichever contract he's under when he's traded. In this case it's going to be his 6-year max deal. However, in the event that Bosh had been traded prior to his last contract expiring, the TPE would have been equivalent to the salary in the first year of said contract.

Everyone still with me? Great!

That's why this S&T works without the Raptors having to take on crummy players. They receive the draft picks which have no monetary value in addition to the TPE which makes the salaries match. Now the Raptors will have exactly 1 year to use their Traded Player Exception.
In terms of using the exception there are limitations. The Raptors may only acquire one player at a time (single-player trades) meaning that they can't use the trade exception on a package of players. Although a team would be able to send draft picks in addition to any said player. Beyond that though, the Raptors are free to split up the trade exception to acquire numerous players. In the event of the trade, the Raptors would send the trade exception to team B in return for player x the benefit being that the Raptors are able to add salary without exceeding the salary cap and paying tax.

Hope that this helps in some way