Intuitive ... without math:
-- "Voltage" is the 'pressure' in a region or in a conductor that makes
electrons want to leave the warm security of the atoms they're bound to,
and go flowing off toward a place where something is drawing them
harder than the atoms are holding them.
Something external has to provide the voltage. Like a battery. Or even
having too many electrons all in one place (static charge, caused by
scuffling across the carpet in bare feet).
-- "Current" is the measure of how many electrons pass some point
every second, in their restless trip toward that place.
If you could see the crowd of electrons streaming past a point in a wire,
and count them, then every time you counted 6,250,000,000,000,000,000
electrons going by, you would report that "one coulomb" of negative charge
had passed. And if you saw that many passing by every second, then
you would report that there is "one Ampere" of current flowing in the wire.
More 'pressure' convinces more electrons to leave home and hit the road.
(Higher voltage directly causes more current to flow in the wire.)
But if the road is very narrow, or full of potholes, then fewer electrons can
get through in a second or in an hour.
(Higher "resistance" reduces the current, like if the wire is very thin, or
it's made of wet spaghetti instead of copper.)
Electrons don't just get an idea into their head one day, to take off and go see
what's at the end of the wire. The voltage has to be there, pulling them away
from their atoms harder than the atom is holding them.
It also takes energy to rip an electron away from its atom, and keep it flowing
through a wire without moving into the spare room and settling down at the atom
a block away. That energy has to come from somewhere ... usually from the battery.
If the battery is strong enough, and the voltage is high enough, and the
resistance of the wire is small enough, and the current is great enough,
and the traveling electrons have enough energy, it's possible for some of
that energy to come bursting out of the wire and go splashing all over the
place.
The energy may leave the wire in the form of heat, and we would look at
the hot wire and call it an electric toaster or a space heater.
Or the energy may leave the wire in the form of light, and we would look at
the glowing wire and call it an electric light bulb.