Submission means accepting the verdict of the judge, even if it goes against us. In most cases only one party can win, so when two parties to a dispute submit to a judge, they must agree that they will be bound by the judges decision whichever way it goes. They might agree to the options of appeal before submitting to the judge. For example, they might agree that to accept an appeal to a group of judges on issues of law rather than fact.
If there is not grounds for appeal, submission means accepting the decision of a judge, even if it goes in favour of the other party.