What is it meant by two different groups in stereoisomerism? I understand there are some properties in an organic compound that allow stereoisomerism.


double bond can't rotate
two double bonded carbon atoms each have two different atoms or groups attached


I'm unsure by the meaning of two different atoms/groups around on each side of the double bond.



With respect to but-2-ene. From my understanding, both sides of the carbon atom have $\ce{-CH3}$ on either side of the double bond so how does this comply with the rule that "Two different atoms or groups attached around each carbon of the double bond"
Stereoisomers are different due to the spatial arrangement of their atoms. 

The picture that you gave has two $\ce{CH3}$ groups on one side. That is called cis - as they are on the same side. There is another isomer, called trans. That is when one of the $\ce{CH3}$ is on the top and the other $\ce{CH3}$ is at the bottom. The arrangements of the $\ce{CH3}$ and $\ce{H}$ is different in cis and trans.

This link explains it well: Chem.Libretexts