A reasonable definition might be:
A molecule is organic if it contains carbon and hydrogen.
Scientists have not agreed on a single definition that covers all organic molecules.
But the above definition will probably cover the vast majority of the compounds you will encounter.
Some exceptions to the rule are compounds like #"H"_2"CO"_3# and #"HCN"#, which are usually considered to be inorganic molecules.
And the rule does lead to some inconsistencies.
For example, #"CH"_3"Cl"#, #"CH"_2"Cl"_2#, and #"CHCl"_3# are all organic, but #"CCl"_4# would be classed as inorganic, even though most scientists classify it as organic.
The important biological molecules such as carbohydrates, lipids, proteins, and nucleic acids are all organic molecules.