Fetching details from the dictionary...
to gush forth (e.g. water from a spring); to flow (out); to stream (out); to bubble up
to well up (of tears, emotions, etc.); to flow out (of tears)
to emerge; to suddenly appear; to come forth
岩の間から清水が湧き出た。
Clear water gushed out from between the rocks.
泉から水が湧き出ていて、地元の人が汲みに来ていた。
Water was flowing from the spring and locals were coming to draw it.
アイデアが次々と湧き出る瞬間が好きだ。
I love those moments when ideas well up one after another.