A profession, or as we usually say, a vocation (1 Corinthians 7:20). The "hope of your calling" in Ephesians 4:4 is the hope resulting from your being called into the kingdom of God.

Noah Webster's New International Dictionary of the English Language

1. (p. pr. & vb. n.) of Call.

2. (n.) The act of one who calls; a crying aloud, esp. in order to summon, or to attract the attention of, some one.

3. (n.) A summoning or convocation, as of Parliament.

4. (n.) A divine summons or invitation; also, the state of being divinely called.

5. (n.) A naming, or inviting; a reading over or reciting in order, or a call of names with a view to obtaining an answer, as in legislative bodies.

6. (n.) One's usual occupation, or employment; vocation; business; trade.

7. (n.) The persons, collectively, engaged in any particular professions or employment.

8. (n.) Title; appellation; name.