Imagine you release a ball from the top of a hill and it rolls down. The taller the hill, the faster the ball will get, the more energy it will have. If the hill is X unit high, the ball get X units of energy.
From conservation of energy, a ball with X units of energy can roll up a hill of height X before coming to a stop. If such ball is rolling on the ground and there is a hill (a “barrier”) of height greater than X in front of it, the ball will climb up X units, stop, and roll back down the same side. But if the hill is less than X tall, then the ball will roll over to the other side of the hill.
What I describe above is classical physics. It’s very intuitive and describe everyday life very well: you can try rolling balls at home too.
You can think of the wall the girl built in the meme as a kind of hill too. If you throw an electron at the wall, it gets repelled by the electrons of the atoms of the wall (in the same way the ball gets “repelled” away from the hilltop by gravity along with the slope of the hill). In classical physics, you can calculate how much energy an electron should need to surmount this repellent force and pass through the wall. This would be the height of the girl’s hill.
But it turns out that even electrons with lower energy can still sometimes pass through the wall. This is the phenomenon of Quantum Tunneling (because the particle cross through the hill without going over the hilltop: it used a tunnel). I can tell you it is a feature of the wavelike behavior of particles as quantum mechanics describe, but if you ask “why do particles have wavelike behavior” then you’ll have to see @model_tar_gz ‘s answer.
The joke in the meme is that the girl thinks she is safe because she has a wall. But considering quantum effects, there can still be particles (knives) that tunnel through and hit her.