what are the best professions for a druid?

and please explain why those professions are the best most useful choices?

I mean it all depends honestly on what you want.

Do you want to make gold?
Mining/Herb and Skining - I wouldn’t recommend both Mining and Herbing together since you can only track one but if you have an eye then you could do it. Instant flight form and travel form make druidamazing for gathering professions.

Do you want to use them for PvE?
Tailoring and Engineering can give the absolute biggest DPS increase, although this requires absolute management of your hyper speed accelerator (Huge haste buff) and the tailoring proc from your cloak while lining them up with your spec CDS. For just static increases BS/JC are the best.

I can’t comment too much on PVP since I have touched WOTLK in 10 years and I’m just getting back into the swing of things.

PvP:

Enginnering > every other profession, any class (haste or rocket for gloves, parachute and nitro boosts on back/feet for BG’s.
Secondary is irrelevant, as the boost from JWC/Tailoring/BS/Enchanting is pretty much the same.

If you are just starting out on server go JC/Ench

First off, you will never lack work. People need those two profs more than any others. Secondly being able to gem and enchant your own gear is fantastic. Thirdly the Dragon Eye gems and ring enchants give a nice edge for whatever end game pursuits you have in mind.

After that its going to depend on what specs you are going for.