The background information in this statement is:
"Mr. Chan has a two-week history of fatigue, shortness of breath, and easy bruising."
This provides the relevant medical history and symptoms that have led up to the current diagnosis. It gives the background of what the patient has been experiencing recently.
The assessment is:
"I believe has acute myelogenous leukemia."
This states the physician's diagnostic impression of what is causing the patient's symptoms based on the findings.
So in summary:
Background: Details about the patient's medical history and presenting symptoms (fatigue, shortness of breath, easy bruising over past 2 weeks)
Assessment: The physician's diagnostic conclusion of acute myelogenous leukemia based on this background information and test results.
Providing the background helps give context for the assessment and current situation. It allows the ER physician to understand what has been going on with the patient leading up to the need for hospital admission. Let me know if you need any clarification on which parts of the statement provide background information versus assessment.