The term "stock-browser" refers to the web browser which usually comes pre-installed with your Android device.
To be more precise, "stock" is a bit ambiguous. So "stock browser" should refer to the browser coming with "plain Vanilla" Android, as it is built by the AOSP Project. Usually manufacturers as well as vendors leave this browser untouched, which lead to the "easier" answer in the excerpt.
However, things may differ, as currently some devices shipping with Ice Cream Sandwich or Jelly Bean seem to use Google Chrome as pre-installed browser (e.g. Motorola's new Razr and probably future Motorola devices as well).