It’s hard to give a comprehensive answer to that, but perhaps just a few points…
When using “my”, “your”… with uncountable nouns (time, water, sugar, education, training, knowledge of languages), you need to insert “cuid” and put the noun in the genitive case:
Mo chuid ama, do chuid uisce, a chuid traenála, bhur gcuid Gaeilge
It’s also common to insert “cuid” when referring to countable nouns in plural:
Mo chuid caranna, do chuid múinteoirí, a chuid duaiseanna
However, as Aonghus pointed out above, “cuid” is not used with plural when referring to certain body parts: mo shúile, do chosa, etc.
In all the above cases, “cuid” has no independent meaning, it just means “my time”, “your water”, “his prizes”, etc.
Apart from that, it’s basic meaning is “part” or “portion”, but also: cuid de na daoine (“some people”), ith do chuid (“eat your fill”), “mo chuid den tsaol” (“my life, my dearest”).
I’m sure others can think of more. 🙂