Q:

Was in the sentence of today

Why was she absent today for the morning class? 
              Is it right? Some one please answer me. l have a doubt about usage of was along with today.

A:

"Was" indicates past tense - something that happened before this sentence was spoken. If it was in present tense ("is"), it would mean the morning class was still in session when this was spoken (i.e.,"Why is she absent today?"). This sentence is being spoken after morning class is over. 
"Today" is also both necessary and grammatically correct. There are multiple points of time in one day (today), so an action done this morning is now in the past. Without "today", we don't know on which day she was absent. (i.e., "She was absent from class." Was she absent yesterday? No, she was absent today.) 

