何（なに）より, or 何（なに）よりも when emphasized, is a common phrase in Japanese that is used when one wants to express that they are ‘glad’, ‘relieved’, or that ‘(A) is more important than anything’. As this structure is simply a combination of the substitute noun 何（なに） ‘what’, or ‘whatever’, and the particle より ‘than’, the closest literal translation is ‘more than anything, (A)’. 何（なに）より is primarily used to express positive feelings when the actual situation may have been worse, but (A) is the most important.
何（なに）より, and 何（なに）よりも most often behave adverbially, meaning that they can be used at the beginning of a sentence, or right before the word they are describing. However, they occasionally come directly before a noun when followed by の.

• 何（なに）より驚（おどろ）いたのは、あの中田（なかた）くんが医者（いしゃ）になったことだ。
  The most surprising thing is that Tanaka-kun became a doctor.
• 田中（たなか）様（さま）のお役（やく）に立（た）てて何（なに）よりです。
  We are glad to be of service to you, Tanaka-sama.
• 何（なに）よりも大切（たいせつ）なのは、何（なん）でも諦（あきら）めずに頑張（がんば）ってやることだ。
  The most important thing is to not give up and to do your best in anything you do.
• 休（やす）みの日（ひ）に妻（つま）とドライブに行（い）くのが何（なに）よりの楽（たの）しみです。
  I love going on drives with my wife on weekends more than anything.

As in most cases, も just strengthens the phrase slightly, with no other significant change in nuance.