Full Idea
The symbol 'aleph-nought' denotes the cardinal number of the set of natural numbers. The symbol 'aleph-one' denotes the next larger cardinal number. 'Aleph-omega' denotes the omega-th cardinal number.
Clarification
'omega' is ω (can't do alephs!). Aleph comes from the Hebrew alphabet
Gist of Idea
'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal
Source
Shaughan Lavine (Understanding the Infinite [1994], III.3)
Book Reference
Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.50