It's a standard term. I'll assume you're familiar with 'cousin' (in the strict English/western sense), aka (rarely, only really in contradistinction) 'first cousin'.
1. Your parents' [first] cousins' children are your 'second cousins';
2. Your parents' second cousins' children are your 'third cousins' (and so on);
3. Your parents' [first] cousins are your '[first] cousins once removed';
4. Your parents' second cousins are your 'second cousins once removed' (and so on);
5. Your parents' [first] cousins once removed are your '[first] cousins twice removed' (and so on).
"once removed" is such a strange term to me. It reads like they become first cousins only once something unspecified was removed. Like "once the tumor was removed the patient survived".
'Removed' is (also) used like degrees of separation, if you're familiar with Bacon or Erdos numbers for example. 'I took the leap into management, but my current role still isn't that far removed from programming'.
The 'once' here means 'one time', not 'when it has happened that'. cf. my 'twice removed' example above.
1. Your parents' [first] cousins' children are your 'second cousins';
2. Your parents' second cousins' children are your 'third cousins' (and so on);
3. Your parents' [first] cousins are your '[first] cousins once removed';
4. Your parents' second cousins are your 'second cousins once removed' (and so on);
5. Your parents' [first] cousins once removed are your '[first] cousins twice removed' (and so on).