A dependant is someone who relies on someone else, possibly for financial support. You'll most often find this spelling in British English, where it's favored (or favoured!) in using the word as a noun.
Don't be confused by the spelling. In the UK, the -ant ending often shows up for the noun but not the adjective. In the US, the -ent ending is more popular for both the noun and adjective. Either way, this word has to do with reliance. Kids are dependants (or dependents) of their parents, which means they depend on them for food and shelter.