What does the AND gate do to prevent electrical current?
It depends on what technology the AND gate is built with. The transistors are used as switches. CMOS technology uses MOSFET transistors which use voltage as the switch control, but other technologies can use current, such as LSTTL with BJT transistors.
If the AND gate is made with BJT transistors, it will have two transistors in series, and both must be on to have current on output. It's basically same as having two light switches in series, as the light will turn on only if both light switches are on.