Step 1: Picture the molecule.
Tetrahydrofuran, or THF, is a small five-membered ring. Four corners are carbon atoms and one corner is an oxygen atom.
Step 2: Homocyclic or heterocyclic.
A ring with only carbons is homocyclic. A ring that has at least one other kind of atom is heterocyclic. Since THF has an oxygen in the ring, it is heterocyclic.
Step 3: What aromatic needs.
To be aromatic a ring must be flat, fully connected with overlapping p-orbitals, and follow Huckel's rule of $(4n+2)$ pi electrons going all around.
Step 4: Look at the carbons.
The word tetrahydro means the ring is fully saturated with hydrogen. All four ring carbons are $sp^3$ hybridised.
Step 5: Why it is not aromatic.
$sp^3$ carbons have no spare p-orbital, so there is no continuous flow of pi electrons around the ring. That breaks the aromatic requirement.
Step 6: Final choice.
THF is heterocyclic and nonaromatic, which is option 4.
\[ \boxed{\text{Heterocyclic nonaromatic}} \]