Opera Presto refers to older versions of the Opera browser - up to version 12.x - which used the Presto rendering engine (before Opera switched to using Blink from version 15 onwards in 2013).
In February 2013, Opera Software ASA announced that their products would transition to using Chromium/WebKit. It was later announced they would actually switch to Blink, the same fork of WebKit used by Chrome. Prior to this, they had been using the now discontinued Presto rendering engine.
The last Presto-based version of Opera is Opera 12, which has only seen security-related minor releases since Opera's main development switched to Blink. The latest version of Opera using Presto is 12.17.
This tag, opera-presto, should be used for questions that are specific to the older Opera powered by the Presto rendering engine; questions specific to the newer, Blink-based version should use opera-blink, while questions not specific to either should use the generic opera tag.