In EU Law - it's again vague to mean different things in different contexts. I reference a few documents here that the UK and EU use, for example, in immigration cases to determine the dependency of a relative (parent/grandparent) coming to be looked after in the UK by their relative.
UK Immigration Application Form for Dependent Relatives Appendix 1: here. Living alone, home ownership, financial support, medical conditions, ability to self-care and availability of others to care for you are asked about.
There is further legislation, pertinent to the free movement within the EEA (rather than non-EU immigration) seen here and the rules here.
UK Immigration Rules EC-DR here - would clarify dependency as:
E-ECDR.2.4. The applicant or, if the applicant and their partner are
the sponsor’s parents or grandparents, the applicant’s partner, must
as a result of age, illness or disability require long-term personal
care to perform everyday tasks.
E-ECDR.2.5. The applicant or, if the applicant and their partner are
the sponsor’s parents or grandparents, the applicant’s partner, must
be unable, even with the practical and financial help of the sponsor,
to obtain the required level of care in the country where they are
living, because-
(a) it is not available and there is no person in that country who can
reasonably provide it; or (b) it is not affordable.
Dependency has been challenged a number of times in the European Courts. The relevant regulation is Regulation 7(1)(c). This provides that for the purpose of the EU Regulations, dependent direct relatives in the ascending line of the spouse or civil partner of the EU national should be treated as family members.
"Applications will usually succeed if enough evidence of material or
emotional support is provided and if it is demonstrated that having
regard to the financial and social conditions, the dependent relative
would not be in a position to support himself/herself without the EU
worker’s help. The need for material support must exist in the state
of origin of the relative, or the state where they came to be at the
time when they joined the community member."
from here.
In Ireland, there are further considerations, beyond the notion of dependency the sponsor has to meet: here
As you can see, it is quite a broad consideration. I hope this helps :)