Discretionary review is a 2nd level of appeal in the Washington State appeals process. If you lose in your first appellate case, then you can request that a higher court accept review of the decision (for Superior Court decisions this means the Court of Appeals, and for Court of Appeals rulings further review is made to the Washington Supreme Court).
However, this next level of review is not automatic. An appeal from a misdemeanor criminal conviction or administrative ruling qualifies only for automatic review to the Superior Court (likewise to the Court of Appeals for felony convictions), and any further appellate review is not guaranteed. Ultimately, it is up to the discretion of the Court whether they hear the appeal, hence the name.
You ask for a review by filing a motion for discretionary review. There are certain guidelines that the appellate courts must follow in deciding whether or not to accept a case, and a large percentage of motions for review are rejected.
One of the reasons the appellate courts are so selective in what issues they choose to address, is that at the Court of Appeals and Supreme Court level decisions can have precedential value, which means they make law that would apply to all courts and future cases.
Generally, the types of cases that are accepted involve issues that are likely to have broad application and are likely to recur in similar cases in the future.
Needless to say, discretionary review is a rare opportunity if it is granted. With the right facts and a good argument, it can be tool for justice for our clients and others.