In my previous life as an Oracle DBA / Developer, I think I understand this question better than people with just a SQL Server background. Other database systems have the concept of a "BEFORE" trigger that occurrs before the actual statement being executed applies changes to the table. SQL Server only has AFTER triggers

Other database systems also allow row level triggers instead of just statement level triggers like SQL Server does, and a row level trigger typically gives you OLD and NEW context variables for each column in the table the trigger is on. Using those context variables in a BEFORE trigger you could actually change the values of data using the trigger. A common use of this would be in a table that has audit columns in it such as LastModifiedDateTime. Setting the NEW context variable for LastModifiedDateTime in a BEFORE trigger would keep the value the way you want it but with only 1 modification of the row in the database. A table with a SQL Server AFTER trigger will actually cause the row to be modified twice, and in SSMS you actually see the message (1 row(s) affected) twice.