A lot of things can confuse people when first learning electronics so don't let it get you down. Binary, logic 1's and zero's are all different terms for ON and OFF. A logic gate is operated either ON or OFF. Each logic gate has different voltage levels as to what is classed as ON. It usually varies between 5V and 12V but there are many other values. You have to consult the data sheet for the logic gate that you are using. OFF is 0V.
Therefore for a 5V AND gate, 1 input at 0V and 1 input at 5V will output 0V. Both inputs at 5V will output 5V. Both inputs at 0V the output is 0V.
I hope this helps.
Keep up with the studying. It will all make sense in the end!
If you consider an AND gate.
If both inputs are "1" then the output is a "1". Simple rule, but very powerful.
But what if you had one input high all the time?
Can you see that what comes out of the output would depend on what is coming into the other input. If it was a stream of pulses, they would come out of the output. If they were high, both inputs would be high so the output would be high. If they were low, one input is high but one is low so the output is low.
Now make that first input a Zero.
Now, it doesn't matter what comes into the other input. Nothing will get sent to the output.
At least one input is low so the output is low.
So, you can control the outputting of that stream of pulses just by putting a 1 or a 0 on the other input. Put a 1 there and they get through. Put a 0 there and they don't.
One other comment. You'll often see TTL applied to certain circuits which stands for "Transistor-Transistor Logic" and means silicon based bijunction transistors which saturate "switch" at 5 volts. This as compared to CMOS (complementary metal oxide semiconductor) which uses FET transistors switching around 3.5 volts.
Think of a transistor amplifier circuit. It can't amplify arbitrarily large signals and hits some maximum voltage (generally the supply voltage). The shape of the output for a given linear input voltage will be a flat line in the negative domain then curving upward (linear amplifying domain) then leveling off at saturation.
Zoom out and this looks like a simple step function indicating the transition from switched off to switched on.
AND gates can be made by requiring two inputs both be on to switch on the output (A FET with two gates or simply two transistors in series (emitter to collector) with the bases being the inputs), inverters by simply constructing inverting amplifiers. With AND and NOT you can construct any other logic.