What does like dissolves like mean?

Polarity is the degree of charge separation in molecules. Polar molecules always have an excess of electrons on one end whereas non-polar molecules have a more symmetrical charge distribution.
Polarity affects interactions between molecules. Depending on whether the participating molecules are polar or non-polar guides the way they interact with each other.
Polar molecules interact with each other by strong attractive whether polar molecules interact with non-polar molecules through dipole- induced dipole interactions ( a weak dipole induced subject to charge of a dipole similar to the way a permanent magnet induces a temporary magnetism on a metal ).
Polar molecules mix easily with another polar molecule and form a homogenous phase / solution whether when they are subjected to mix with a non-polar molecule they stay as separate phases and don’t dissolve into each other. This gives rise to the term “like dissolves like”.

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