I know "jump off the deep end" means to abruptly step into something but I'd like to know what it means in terms of actual physical jumping - because you usually "jump off" something not deep. What does a native speaker imagine when hearing the phrase?
The relates to jumping (or diving) into the deep end of a swimming pool.
In the deep end of the pool, the water is too deep for you to stand on the bottom, so you are forced to swim. It's a metaphor for coping with the unfamiliar, especially when you are not properly prepared. "Deep water" is a metaphor for the unknown, so when you jump into deep water you don't know what might happen, or what might be lurking under the surface.
A related idiom is sink or swim. When you jump off the deep end, you have choice but to learn to swim, otherwise you're going to drown.
In addition, go (or jump) off the deep end has become synonymous with go crazy, or lose one's head:
lose one's head (v), "To behave irrationally or to lose self-control, especially in a distressing situation"
The connection here to swimming pools is less clear, although it's probably connected with the idea of deep water being (literally) unfathomable, meaning that you have no idea what someone who has "gone off the deep end" is going to do.