The main Di definition when the word is by itself comes from the world of music. In the solfege system, Di is the half-step between Do and Re on a chromatic scale.
Another Di meaning as a standalone word is when it shortens a proper name, Diana. The people of England used this Di abbreviation when they referred to Princess Diana of Wales simply as Princess Di.
A more common Di meaning is when it acts as a prefix meaning two. For example, in carbon dioxide, the di- means that there are two oxygen molecules in the compound. The DI abbreviation is used to refer to a number of aspects in the business, medical and technological worlds.
At a hospital, it might be shorthand for the diagnostic imaging department.
In technology, the DI definition is direct input.
The educational Destination Imagination group often goes by its initials, DI.
(in the UK) Defence Intelligence.
(in the UK) Detective Inspector.