This seems to say that the Crown appealed from a verdict of acquittal in a criminal case. It is reported to be a judge, not a jury, that acquitted the defendant. Would that mean that this was a bench trial, or just that the judge decided that the defendant should be acquitted even if the facts were as alleged by the Crown so that no jury deliberations were needed? Are verdicts of acquittal in Canada generally appealable, or might that apply only to bench trials, or otherwise only to acquittals by a judge rather than by the jury?
Part XVIII of the Criminal Code addresses the power and procedure for appeals. Appeals of indictable offences are appealed to the provincial Court of Appeal.
The Crown can generally appeal where there is an error in law. The Crown has a limited appeal on the basis of questions of fact. This includes appeals for unreasonable verdict.1 However, the Crown cannot appeal on issues of credibility unless it amount to an error in law.
The Defence can appeal both issues of fact and law.(ss. 675 and 676)
R. v. Kendall,  O.J. No. 2457 (Ont. C.A.), at para. 46
from a Canadian Criminal Procedure Wiki.
Unlike in U.S. law, the government can directly appeal an acquittal on certain grounds in Canada (without regard to whether it was a jury trial or a bench trial), although those grounds aren't quite as broad as those of the defense. This would also be true in modern English law.
In practice, it is somewhat easier to appeal a verdict in a bench trial than in a jury trial, because in a bench trial you know why the judge says he or she came to the verdict and can determine if those reasons were incorrect, while in a jury trial, the appellate court presumes that the jury followed the law and use any even implausible basis for their opinion even if that isn't what really happened.
The complete bar on appeals of acquittals of criminal charges in U.S. law due to the double jeopardy clause of the U.S. Constitution's Bill of Rights, is a rare exception to the global norm.
Acquittals are generally appealable in Canada on questions of law alone, though I would like to point out that there are two levels of appeal in R. v. Jarvis and though the requirements for both are similar in this circumstance, they are technically distinct.
Section 676(1)(a) of the Criminal Code governs the Crown's ability to appeal an aquittal from a trial court to a court of appeal:
676 (1) The Attorney General or counsel instructed by him for the purpose may appeal to the court of appeal
(a) against a judgment or verdict of acquittal or a verdict of not criminally responsible on account of mental disorder of a trial court in proceedings by indictment on any ground of appeal that involves a question of law alone;
Paragraph 20 of the appeal decision confirms this was the route taken in R. v Jarvis. Note that the Crown has no right of appeal for questions of fact or questions of mixed fact and law, it must be one of law alone.
Section 693(1) governs the Crown's ability to appeal an acquittal from a court of appeal to the Supreme Court of Canada (SCC):
693 (1) Where a judgment of a court of appeal sets aside a conviction pursuant to an appeal taken under section 675 or dismisses an appeal taken pursuant to paragraph 676(1)(a), (b) or (c) or subsection 676(3), the Attorney General may appeal to the Supreme Court of Canada
(a) on any question of law on which a judge of the court of appeal dissents; or
(b) on any question of law, if leave to appeal is granted by the Supreme Court of Canada.
Again, appeal is only available on questions of law alone, though this is less obvious with the lack of the word "alone." In R. v. Biniaris paragraphs 30-31, the SCC held there was no distinction between "questions of law" and "questions of law alone."
In R. v. Jarvis, subsection (a) applies due to dissent in the court of appeal as confirmed by paragraph 4 of the SCC decision. Otherwise, leave would have had to be granted at the discretion of the SCC according to subsection (b).
Incidentally, all of this is independent of whether the trial was by jury or not.
All of the above is for indictable offences which is the case in R. v. Jarvis (roughly equivalent to a felony in the US). I didn't spend too much time researching summary conviction offences (roughly equivalent to a misdemeanor in the US) because, well, they're more complicated with references scattered in the law. As far as I can tell, it appears that Crown summary conviction appeals may not be restricted to questions of law and that they may require leave where indictable appeals don't. If you're feeling adventurous, here are some references I read through before giving up: Criminal Code s. 676(1.1), ss. 812-839, Supreme Court Act ss. 37 & 40, R. v. Helm.
As to the double jeopardy issue raised in ohwilleke's answer, Canada also has constitutional protection against double jeopardy through Charter s. 11(h), but this only applies after final verdict (i.e. after appeals are exhausted).