This verse is a simple statement of fact. It means that David, after being anointed king over the tribe of Judah, ruled from the city of Hebron for a period of seven years and six months.

Here's a breakdown:

"The time that David was king in Hebron...": This specifies the location (Hebron) and role (king) during the period being described.
"...over the house of Judah...": This clarifies that initially, David's kingship was limited to the tribe of Judah, not the entire nation of Israel. Other tribes didn't immediately accept him as king.
"...was seven years and six months.": This is the duration of David's reign in Hebron.

Significance:

This verse is important because:

It marks the beginning of David's reign as king. While Saul was the previous king of all Israel, his death created a power vacuum. David's anointing and subsequent rule in Hebron was a crucial step in his eventual ascendance to the throne of all Israel.
It highlights the fractured nature of Israel after Saul's death. It took over seven years before all the tribes accepted David as their king. This period was marked by conflict and political maneuvering.
It provides a timeframe for events that occurred during this period. Understanding the length of David's reign in Hebron allows us to better understand the context of other stories and events that happened during those years, such as his relationship with Abner and Ishbosheth.

In short, the verse is a chronological marker, stating the length of David's rule over Judah from Hebron before he became king over all of Israel.