This phrase is a metaphor that compares the speaker to oxygen and the person they are speaking of to someone who is desperate to take a breath. The speaker is suggesting that they have an important role in the other person’s life, and that their presence is necessary in order for the other person to thrive. In other words, the speaker is emphasizing their importance to the other person and the level of importance the other person has placed on the speaker by wanting to breathe in their presence.