Does the World of Warcraft character boost upgrade both professions?

When you get a character boost in World of Warcraft - either by pre-ordering the expansion or by purchasing it in the shop - if you boost a character who is level 60 or higher, you get to level up "Primary" profession for free.

By this does it mean only one profession, or both professions?

From here:

If the character is at least level 60 before the boost, their primary professions and First Aid will be leveled up to rank 600. Other secondary professions will not be affected.

So skills like enchanting and tailoring will be upgraded. Professions like fishing and cooking however are not upgraded.

And from here

Characters who are already at or above level 60 will also have their existing primary professions and First Aid skill boosted to 600 skill level

That is even more clear

If you have no professions selected, they will be chosen for you. That depends on the type or armor you can wear:

• Plate: Blacksmithing and Mining
• Mail or Leather: Leatherworking and Skinning
• Cloth: Tailoring and Enchanting

Main professions and First aid will be upgraded If your character is level 60 or above. If you don't have any main professions you will be grated some based on the armor-type your class has. These are:

• Enchanting, Tailoring for Cloth Classes (Priest, Mage, Warlock)
• Skinning, Leatherworking for Leather / Mail Classes (Monk, Rogue, Druid, Shaman, Hunter)
• Mining, Blacksmithing for Plate Classes (Warrior, Paladin, Deathknight)

Fishing, Cooking and archeology will not be upgraded to level 600 (But those are rather easy to level).

You can find the full FAQ to character boosts here.