You can use CROSS APPLY
:
SELECT [Date]
, API
, LEFT(col,CHARINDEX('_',col)-1)'Latency'
, RIGHT(col,CHARINDEX('_',REVERSE(col))-1)'Aggregation'
, Value
FROM
(
SELECT [Date],API,col,value
FROM YourTable
CROSS APPLY
(
VALUES ('Latency1_Avg', [Latency1_Avg]),('Latency1_Min', [Latency1_Min]),('Latency1_Max', [Latency1_Max]),('Latency2_Avg', [Latency2_Avg]),('Latency2_Min', [Latency2_Min]),('Latency2_Max', [Latency2_Max])
) C (COL, VALUE)
) SRC
Demo: SQL Fiddle