The problem here is that the value of a lookup field is not actually a string (as displayed in the UI) but an ID, so when you perform your SOQL query you are comparing an ID to the Name field and getting no results.
If you change your code to the following you should get the result you expect.
It should also be notified that this simple use case could also be accomplished using a simple Workflow Field Update rather than a trigger.
trigger UpdateYield on Account (before update)
{
Set<Id> HS = new Set<Id>();
for (Account hsName : Trigger.new)
{
if (hsName.High_School_LU__c != null)
{
HS.add(hsName.High_School_LU__c);
}
}
Map<Id, High_School__c> y = [SELECT Name, Yield__c FROM High_School__c WHERE Id IN :HS];
for (Account YieldU : Trigger.new)
{
High_School__c a = y.get(YieldU.High_School_LU__c);
if (a != null)
{
YieldU.Yield__c = a.Yield__c;
}
}
}