According to the dictionary, they both mean 'some'.
Quelque(s) is an indefinite determiner, translatable as "some" or "a few". It's always attached to a noun phrase: Il y a quelque temps (some times ago); J'ai bien quelques idées, mais... (I have a few idea, but...); Je suis parti en vacance avec quelques amies (I went on holyday with a few friends (f.))
Quelques-un(e)s is an indefinite pronoun. It stands alone, in place of a noun phrase, and can refer to animates and inanimates both. Il y en a toujours quelques-uns qui n'ont pas d'appétit (There's always a few that don't have any appetite); Des voitures sans plaques ? J'en ai vu quelques-unes, mais pas tant que ça (Plateless cars? I saw a few, but not that many). The singular is quelqu'un, which, like its English counterpart someone, can only be used to refer to a human being. Otherwise you use un(e), much like you'd use one in English.
Chaque and chacun have a similar relationship, as do mon and le mien (and the rest of the possessives), or tous les /tulɛ(z)/ and tous /tus/. Note that English generally has a different word for each member of of these determiner/pronoun pairs (each/each one; my/mine; every/everyone). "Some" is a bit of an exception.
Both quantify countable objects. Both qualify several but small amount of objects
The difference is mostly about the construction of your sentence.
quelques-uns is used to refers to another stuff.
"J'ai pris quelques pommes dans le jardin, tu en veux?"
"Non merci, j'en ai déjà mangé quelques-uns"
quelques means "some" without any kind of explanations.
The speaker picked up somme apples.
quelques-uns is built with
en refers to the apples, and
-uns refers to
en. they have exactly the same meaning, the second speaker could have answered :
"Non merci, j'ai déjà mangé quelques pommes"
Both answers have exactly the same meaning. But frenchs hate redundancies, so he tries not to repeat "apple" to refers to the same object
Another example :
"Il me faudrait quelques-uns de tes hommes"
uns refers to hommes
"Tu as des vis?
"Il m'en faudrait quelques-unes"
unes refers to en refers to vis (a screw) =feminine