In the context of the ACID principles (see also ACID transaction) for database transactions "Isolation" denotes the idea that concurrent transactions must not see intermediate (i.e. uncommitted) results of each other. One could also say that transactions don't notice any concurrent transactions, i.e. they are isolated from each other.

In classic database theory isolation is maintained by allowing only serializable schedules of transactions. This means that it must be possible to reorder the actions of all transactions in the schedule in such a way that a serial schedule with the same effects results. A schedule is serial if all transactions are executed completely one after another.

The isolation principle becomes a problem for 'advanced' database applications like CAD which feature so called long transactions. Since long transactions normally take hours or days to complete, guaranteeing isolation between concurrent transactions is difficult and often not wanted. If several developers are working at a common model, it may be advantageous if their transactions are not isolated but the developers can see each others intermediate results early. Therefore different grades of isolation were introduced from which database users should be able to choose:

degree 0: Chaos
Does not overwrite dirty data of other transactions but provides no other protections. This can be achieved by setting short exclusive locks on written (i.e. dirty) data.
degree 1: Browse
In addition to degree 0 this degree provides protection against lost updates. This can be achieved by setting long exclusive locks on written data. Therefore written data becomes visible only after the transaction ends.
degree 2: Cursor stability
In addition to degree 1 this degree does not read dirty data. This can be achieved by setting short shared locks on read data. This isolation degree is used by most commercial RDBMSs.
degree 3: Isolated serializable repeatable reads
In addition to degree 2 this degree ensures repeatable reads, i.e. other transactions don't overwrite data read by this transaction. This can be achieved by setting long shared locks on read data.

Degrees 0 and 1 allow to read without setting any locks. This allows early read access to intermediate results but may lead to cascading aborts if no further precautions are taken.

The four degrees of isolation are mentioned in the book Transaction Processing: Concepts & Techniques by Jim Gray and Andreas Reuter, 1993 and probably elsewhere