There is an equation that describes the most likely place that a given electron will be at any one point in time. We call this equation the wavefunction. For the 1s electron, the wavefunction tells us that it will most probably be in a circle of a certain radius.
Now this circle is not just a line, it has a thickness too. We can imagine it as a big grove cut into the ground, such that its cross section would look like a half pipe, at a skate park. If we imagine the electron as a skater, going round this halfpipe, there will be times when the skater is on the coping or ‘walls’. This is allowed and is perfectly fine, but the skater can not leave the halfpipe without adding in some extra effort. But the majority of the time the skater will be in the bottom half of the half pipe.
This is how a wavefunction works. It says that sometimes the electron can be on edge (the walls or coping) of its orbit but must not leave it without extra energy (effort from the skater) being used. Furthermore, the wavefunction also says that most of the time the electron will be in the deepest part of its orbit (the bottom half of the half pipe).
Combining these two restrictions together we can see that most of the time the electron will maintain an almost perfect circular path around the nucleus. So because the electron never stops moving if we average out its position over all time it simply gives a circle around the nucleus. This is what is trying to be drawn when you look at the stereotypical picture of an atom, showing the nucleus with rings around it at different angles.