After many bench trials or the hearing of motions, the judge often will issue findings of fact and conclusions of law, especially if requested to do so by a party.
These set forth the facts the judge found to be true and the conclusions of law he reached regarding those facts. This allows a losing party to know how and why the judge reached his decision and whether an appeal is warranted.
If the losing party appeals, the appellate court will determine whether the factual findings are supported by the evidence and whether the legal conclusions are correct. If the court answers either question in the negative, the case will usually be reversed and sent back to the trial court for a new trial.
The lower court is sometimes required to issue such findings for there to be a valid judgement. In the case of some motions, e.g., ones for federal R11 sanctions, the lower court's failure to issue such findings will result in a differing standard of review by an appellate court when it reviews the lower court's ruling, e.g., 'de novo' rather than 'abuse of discretion'.