WITH SAMPLE 50 PERCENT it works as though for each data page in the table SQL Server flips a coin. If it lands heads then it reads all the rows on the page. If it lands tails then it reads none.
UPDATE STATISTICS T WITH SAMPLE 50 PERCENT call in Profiler shows the following query is emitted
SELECT StatMan([SC0], [SB0000])
FROM (SELECT TOP 100 PERCENT [SC0],
step_direction([SC0]) OVER (ORDER BY NULL) AS [SB0000]
FROM (SELECT [C] AS [SC0]
FROM [dbo].[T] TABLESAMPLE SYSTEM (5.000000e+001 PERCENT)
WITH (READUNCOMMITTED)) AS _MS_UPDSTATS_TBL_HELPER
ORDER BY [SC0],
[SB0000]) AS _MS_UPDSTATS_TBL
OPTION (MAXDOP 1)
TABLESAMPLE SYSTEM (5.000000e+001 PERCENT) is responsible for the sampling and is documented here
TABLESAMPLE SYSTEM returns an approximate percentage of rows and
generates a random value for each physical 8-KB page in the table.
Based on the random value for a page and the percentage specified in
the query, a page is either included in the sample or excluded. Each
page that is included returns all rows in the sample result set.
The documentation also states
Although the plan shows a table scan is performed, only those pages
that are included in the result set are actually required to be read
from the data file.
STATMAN call is to an internal aggregate function briefly described here