Definition of action of quantum hamiltonian, two state system

[theidiot]

Homework Statement

Consider a two-state system. We denote the two orthonormal states by |1>and |2>. The Hamiltonian of the system is given by a 2 × 2 matrix:
[omitted in this post, has 4 entries of course, not very interesting]
Write the action of H on the states |1> and |2>.

2. The attempt at a solution

Well, I don't know what is meant by action here! No doubt it's simple but I need to know what 'action' means in this context. Thanks for assistance!

 

[theidiot]

Just to clarify, 'H' is the Hamiltonian and is represented by a 2x2 (hermitian) matrix. I have not explicitly written out the matrix in these posts because there is no need. No reply yet, so just thought to clarify that the 'H' referred to is the matrix of the Hamiltonian. What is meant by its 'action' on the two orthonormal states of the two state system?