This may sound confusing, but draft picks in baseball can not be traded, but Competitive Balance Lottery (CBL) picks can be traded.
Twenty teams every year are eligible for the CBL. The 10 smallest markets (so this will never include the Diamondbacks because Phoenix is much bigger than most MLB cities) and the 10 lowest revenue clubs (this will almost always include the Diamondbacks because of the poor fan support) are entered into a lottery to win 12 picks. The first six picks are Round A and the second six are Round B. In the NFL they're called "sandwich picks" because they're between rounds. In MLB, Round A is right after the second round of the regular June draft (officially called the Rule IV draft) and Round B is right after the third round. In the 2013 lottery for the 2014 draft, San Diego won the first pick of Round B and the Diamondbacks have the second pick right after them.
Now the Diamondbacks have the Padres' pick, giving them four of the first 70 picks.