to pour out: to make a liquid (or, by extension, earth) flow out of where it was held
The plain picture behind this word is tipping a container and letting its contents run out: water emptied on the ground, blood drained at the base of the altar, a drink offering poured before God. Because the action is so vivid, the Bible reaches for it again and again to describe things that are not liquids at all.
When God is the one pouring, the object is his anger or his Spirit. To pour out wrath is to release it fully and unrestrained, the way a tipped jar empties all at once rather than a trickle, and nothing is held back. The same full outpouring turns to blessing when God pours out his Spirit on all people, lavishing it without measure.
When a worshiper is the one pouring, the object is often the self: the heart, the soul, the complaint. To pour out the heart before God is to hold nothing inside, to lay the whole inner life open in prayer. The same verb that empties a vessel describes a person emptied of everything kept private, and even scorn can be poured out, disdain heaped over someone like a spilled liquid.
One further use keeps the literal flavor but turns it to dry material: to pour out earth and rubble against a city wall, heaping up the ramp an army builds to mount a siege. Here the pouring is of soil rather than water, but the motion is the same.