It's probably more important what database you're using. As you don't say, I'll give generic advice. If you comment, I'll try to give more specific help.
There should be a couple of areas you should look at. First of all, if the database is on the same host as the application, configure the database to only bind to the loopback interface. This means that the database is not accessible over the network. You would have to be on the local machine to access it. This will not prevent local users or someone who has hacked into the machine. If the database is on a remote server, look at restricting access from just the application server. If you don't trust the network between the hosts, investigate using SSL for the connection.
Secondly, check your permissions that are granted to individual users. Most database servers have a very flexible set of permissions that you can grant or revoke from individual servers. If you only need a user to read from the database, only grant them SELECT privileges. There shouldn't really be any reason why the webapp needs the ability to change the schema, so don't give them the ability to use CREATE, CHANGE or DROP.
If you can't access the database remotely, there is no benefit in using a strong password for your user.
One thing you should be very careful about is auditing your PHP to prevent SQL injection attacks against your database. This is easy to forget in PHP as it doesn't do much to help you. Other languages tend to use placeholders, which make this type of attack almost irrelevant.