How do I count the total of number of participants in this way?

You can use sum() with subquery :

SELECT description, COUNT(1) as Cnt
FROM Table1
GROUP BY description
UNION ALL
SELECT 'SUM', SUM(Cnt)
FROM (SELECT COUNT(1) AS Cnt
      FROM Table1
      GROUP BY description
     ) C;

However, in SQL Server you can use rollup :

SELECT ISNULL(description, 'SUM') AS description, COUNT(1) as Cnt
FROM Table1
GROUP BY description WITH ROLLUP;'

Based on sample output you are looking for window function :

select description, SUM(number_of_participants) OVER (PARTITION BY groupId), groupId
from Table1;

You can use sub-query if window function not supports :

select t.description, 
      (select sum(t1.number_of_participants) 
       from table1 t1 
       where t1.groupid = t.groupid
      ), t.groupid 
from Table1 t;