A problem with many JDBC drivers is that only one thread can use a Connection at any one time --- otherwise a thread could send a query while another one is receiving results, and this could cause severe confusion.
The PostgreSQL JDBC driver is thread safe. Consequently, if your application uses multiple threads then you do not have to worry about complex algorithms to ensure that only one thread uses the database at a time.
If a thread attempts to use the connection while another one is using it, it will wait until the other thread has finished its current operation. If the operation is a regular SQL statement, then the operation consists of sending the statement and retrieving any ResultSet (in full). If it is a fast-path call (e.g., reading a block from a large object) then it consists of sending and retrieving the respective data.
This is fine for applications and applets but can cause a performance problem with servlets. If you have several threads performing queries then each but one will pause. To solve this, you are advised to create a pool of connections. When ever a thread needs to use the database, it asks a manager class for a Connection object. The manager hands a free connection to the thread and marks it as busy. If a free connection is not available, it opens one. Once the thread has finished using the connection, it returns it to the manager which can then either close it or add it to the pool. The manager would also check that the connection is still alive and remove it from the pool if it is dead. The down side of a connection pool is that it increases the load on the server because a new session is created for each Connection object. It is up to you and your applications' requirements.