“Our success was largely due to Adele's contributions.”

Your former employee is applying for a new job and has asked you to write a letter of recommendation. In your letter, you're describing a project that she was really helpful with. You have described how successful that project was, so now you write:

Our success was largely due to Adele's contributions.

largely

"Largely" means "mostly". It's a more formal word which people use in writing or when trying to sound smart in a discussion. Words that commonly appear after "largely" include:

largely because of ___

largely due to ___

largely ignored

largely unknown

(something) is due to (something)

"Due to ___" explains expresses the cause of something. In the example above, Adele's help "caused" the project to be successful, so the speaker says "Our success was largely due to Adele's contributions."

You use "due to" in slightly formal situations. For example, an announcement on a train might include "due to ___":

Due to construction, the uptown 1 train will not be stopping at 50th Street, 59th, or 63rd. The next stop is 72nd Street.

The thing that follows "due to ___" should be a noun. As another example, if something happened because it's raining, you don't say "due to it's raining". You have to use a noun:

The game has been postponed due to rain.

(someone's) contributions

Your "contributions" are the things that you give to a group project or effort. Your "contributions" can be money, work, or even opinions and ideas.

In the example above, "Adele's contributions" probably means the good ideas that Adele suggested.