Get last modified date of table in postgresql
There is a way with Postgres 9.5 or later. Turn on track_commit_timestamp in postgresql.conf and restart the DB cluster. Starts logging commit timestamps.
Then you can get the timestamp of the latest modification (latest commit) for a given table using the function pg_xact_commit_timestamp():
SELECT pg_xact_commit_timestamp(t.xmin) AS modified_ts
FROM   my_table t
ORDER  BY modified_ts DESC NULLS LAST
LIMIT  1;

NULLS LAST is necessary while there still may be rows without recorded commit timestamp.
Related:

PostgreSQL sort by datetime asc, null first?
Row with latest timestamp
Is there way to get transaction commit timestamp in Postgres?

For Postgres 9.4 or older, see:

How to find out when data was inserted to Postgres?