The server (database/web) can't initiate a connection--only the client can. So you will have to poll the database until there is an update. You can create a web service that checks the database and which jQuery uses.
Edit: I stand corrected. It is possible to keep an AJAX connection open until the server "pushes" data to it. See: http://en.wikipedia.org/wiki/Reverse_Ajax
And apparently it really is polling: http://en.wikipedia.org/wiki/Push_technology#Long_polling. If the server doesn't have any data to send yet, it keeps the connection open until it does. It's not "pure" push technology, because the client doesn't have a listening port which the server connects to. The effect is similar, however.
Edit 2: So back to answering your question... You'll have to choose how to "poll" the web service. The web service would then have to check the database to see if there were updates. Checking the database for updates might be the trickiest and really depends on your requirements. You can run a SQL query to see if anything changed, but how would you know? You would need some sort of parameter (typically a date) to compare against. If done wrong, you could miss some updates or have multiple hits for one update. What Autocracy said would be a good way to get notified of updates. You can keep that list in the database, in memory, etc. and clear it when the client gets the updates.