Many-worlds interpretation says there are lots of worlds in reality. Here I will explain what many worlds interpretation is.
For example, suppose you are observing one electron which is inside a small box. If the box is as small as a sugar cube, this electron can be regarded as it is following the classical physics. But if the box is really small - almost as small as the electron's "orbit" or "orbital" - it is very difficult to determine where the electron is precisely.
Actually it's impossible to determine where the electron is in the orbit. Location of the electron is not determined until you open the small box and check the location of the electron (Only probability of where the electron is can be expected by calculation). When I say "the location is not determined," it is not really determined - The electron exists just as "cloud of probability." [1][2] Thus electron's "orbit" is not really orbit anymore - this is the reason why it's called "orbital" in quantum physics.[3]
We can't expect where the electron really is before we open the box and check where the electron is. This is not because the theory is imperfect, on the contrary, the electron is really cloud of probability before being checked the state. The state of electron is described by wave function.
In many worlds interpretation, this wave function can be applied to the observer (although in Copenhagen interpretation, you can't apply it to the observer). Our body consists of a lot of atoms and electrons which follow the physical rules. If we apply wave function to the body of the observer, state of the observer and the electron which is inside the small box should be uniquely determined.
If we apply wave function to the observer and the electron being inside the box, we will find that many states are existing simultaneously and every time we observe an object, branches of the state are spawned.
We suppose you would decide to go home from the laboratory if you find the electron at right side of the box, but decide to stay at the lab and keep studying there if you find the electron at left side of the box. Both of the states (or worlds) exist in reality. But you can perceive only one state out of the many states.
[1] Purdue university, Chemical Education Division Groups, http://chemed.chem.purdue.edu/genchem/history/schrodinger.html.
[2] "The life and death of stars", http://www.weinberg.northwestern.edu/web/faculty/, Weinberg college of arts and science.
[3] "What is the difference between an orbit and an orbital?", 2016, Quora, https://www.quora.com/What-is-the-difference-between-an-orbit-and-an-orbital
Reference
[1] Toshifumi Sakaguchi, http://quantum.la.coocan.jp/tutorial.html
[2] Toshifumi Sakaguchi, http://quantum.la.coocan.jp/index_eng.html
