What do these statements mean in the MS β exam 70-461 "skills measured" list?
DML - refers to data manipulation (update, insert, delete). A DML trigger is a trigger created to happen on update, insert or delete of table data. 


The update function is the part of a DML trigger where you test if a required update has occured.

For Example:

CREATE TRIGGER myupdate_trigger
ON mytable
FOR UPDATE AS
if UPDATE(column_1)
BEGIN
-- Do something
END


This will trigger a further action every time column column_1 is updated in table mytable. The update function is UPDATE(column_1).