explain why the hydrogen atoms in a hydrogen gas molecule form nonpolar covalent bonds but oxygen and hydrogen atoms in water molecules form polar covalent bonds

Covalent bond:

It is formed by the sharing of electron pair between bonded atoms.

The atom with larger electronegativity attract the electron pair more towards itself and becomes partial negative while the other atom becomes partial positive.

Non polar covalent bond:

It is the bond where both bonded atoms share the pair of electron equally.

For example:

Hydrogen gas (H₂) is non polar covalent compound because the electronegativity of both bonded atoms are same. No poles are created that's why this is non polar covalent compound.

Polar covalent bond:

It is the bond where both bonded atoms share the pair of electron unequally.

For example:

In water the electronegativity of oxygen is 3.44 and hydrogen is 2.2. That's why electron pair attracted more towards oxygen, thus oxygen becomes partial negative and hydrogen becomes partial positive and bond is polar.