1)Because she needed some money to buy a book, she cashed a check.
2)Needing some money to buy a book she cashed a check.
Are these two sentences different??
No they're not.
often an "ing" phrase at the beginning of a sentence, give the meaning of "because".
In second sentence "because" is a omitted. but the meaning of two sentences are the same. you can omit "because" and start a sentence with "ing" which means because.
Now it is your turn can you give me some examples??