Hydrogen bonding takes place between the hydrogen atom of one molecule and an electron pair on a different atom of that same molecule. Hydrogen bonding will occur where partial positive and negative charges can form within a neutral molecule because of differences in electronegativity between the atoms within the molecule.
The most common example is in water where the hydrogen atom of one water molecule can form a hydrogen bond with the oxygen of another water molecule. This can happen because the strongly electronegative oxygen atom draws the bonding electrons toward itself and away from the hydrogen atoms.
A primary amine is neutral overall but can form hydrogen bonds between its own molecules in a fashion similar to water. The nitrogen is partially negative and the hydrogens are partially positive.
A tertiary amine can be a hydrogen bond acceptor with another type of molecule but not with itself since it has no hydrogen atoms around the nitrogen.
Since hydroxyl is a hydrogen bond donor it is not considered a hydrogen bond acceptor.