There are probably several independent sources for the surname Reisner. For the German-Swedish Christian Reisners, it has been said that the name might come from the German reisen, to travel, but the proper form for a traveller should actually be Reisender which leaves this theory in doubt. Other thoughts are welcome.
Among Jews, the surname seems to appear in three major clusters: Latvian-Lithuanian-Belarusian, Austrian-Galician and Hungarian. In the Lithuanian case, the name would seem to be a toponym referring to someone from Rayzn, a Yiddish term denoting an area now roughly southern Lithuania and northern Belarus (more or less the former Grodno Gubernia). A person from Rayzn would be a Rayzner = Reisner. Similarly, in the Galician case, there is an area of Ukraine known as Ruthenia. It, too, was known in Yiddish as Rayzn, hence the Galitzianer Reisners. The Hungarian case remains unclear, but it likely originated as an extension of the Galitzianer Reisners.
Any alternative explanations are more than welcome.