We can't explain the universe, just describe it; and we don't know whether our theories are true, we just know they're not wrong. >Harald Lesch
Moose explained the basic concepts pretty well but I'll give some additional info.
First of all never make Current Player a trigger owner. In ScmDraft it is possible to give triggers to Current Player, but StarCraft would ignore the trigger because it doesn't make sense (in sc logic).
The only valid trigger owners are Player 1 through 8. You can give All Players or a force triggers but what that does (during runtime, when the map is played) is creating copies of the trigger for every player belonging to that group.
So you have 1 trigger owned by All Players and when the game starts there's human players 1-4 and a computer player 8. That means the 1 trigger will exist 5 times, one for each player, which is the same result as if you had ticked player 1 through 8 individually (or in that case because 3 players are missing, ticking P1-4 and P8 would've yielded the same result)
A word on the 3 trigger parts: Owner, conditions, and actions
:
Owner just says who is going to run the trigger. A trigger may have multiple owners, but then the trigger will be executed multiple times. Keep that in mind when dealing with events that should create only 1 response.
Conditions will be checked from top to bottom until one returns false. Only if all conditions returned true the triggers will be executed. When the trigger is owned by another player that other player will wait with his trigger execution until all of the preceding player's triggers have been processed and then he'll check the conditions
again. So when an action from P1's copy of the trigger invalidates the conditions P2 can't run the trigger even though they depend on the same conditions.
Once a trigger starts executing its actions it will execute all actions in sequence, even if one actions makes one or more of the conditions false.
To understand how it works for displaying text I shall make an example:
First an example that might be intuitive, but
won't work:
Force 1Force 1 brings at least 1 [Hero] to 'Inn'Move all [Hero] of Force 1 to 'Inside'Display Text for Current Player "Hello Folks! ..." It will move the group inside the Inn, but only the first player of the force will be shown the text because a display text actions is only working for the Current Player (the player who is currently running the trigger).
Assuming Force 1 consists of P1, P2, P3 and P4, Player 1 will execute the trigger, because as Moose pointed out he's the one who gets to run their triggers first. In StarCraft there is no such thing as running a trigger at the same time. It's all processed in sequence.
So P1 will teleport the group inside and receive their text. When it's P2's turn to execute their trigger there will no longer be a unit at the outskirts of the 'Inn' so he won't run the trigger and thus receives no text.
To rectify the issue the standard technique is to seperate
global actions (move all units) and
current player actions (display text) and
link them with a death counter:
Force 1Force 1 brings at least 1 [Hero] to 'Inn'Move all [Hero] of Force 1 to 'Inside'Set Deaths of Cantina to 1 for Force 1 Force 1Current Player has suffered exactly 1 death of CantinaSet deaths of Cantina for Current Player to 0Display text for Current Player "Hello Folks! ..." Not how I'm using Force 1 in the global trigger and Current Player in the current player trigger. Basically you have to keep in mind that when you're using Current Player you're only affecting 1 player of a group of players.
Technically you wouldn't need Forces or Current Player, but it by using them you don't have to write 8 individual triggers when you want it to be the same for every player.