Your query can be rewritten like this:

SELECT A.activityCode

,A.ActivityName + ISNULL(A.description, '') AS ActivityName

,A.displayOrder

,A.activityStartDate

FROM Activities AS A

LEFT JOIN Activities AS FA

ON A.fatheractivityIncId = FA.activityIncId

AND A.fatheractivitySqlId = FA.activitySqlId

AND FA.isDeleted = 0

AND A.isDeleted = 0

LEFT JOIN Activities AS GFA

ON FA.fatheractivityIncId = GFA.activityIncId

AND FA.fatheractivitySqlId = GFA.activitySqlId

AND GFA.isDeleted = 0

LEFT JOIN Activities AS GGFA

ON GFA.fatheractivityIncId = GGFA.ActivityIncId

AND GFA.fatheractivitySqlId = GGFA.activitySqlId

AND GGFA.isDeleted = 0

That way of putting ON clauses one after another is a bit confusing indeed. It is used when mixing INNER and OUTER joins, but there are clearer ways of expressing the same query.