Can someone please explain singlets and triplets from quantum

They don't actually spin. The particle of the collapsed wave function has angular momentum or something like that, and we call it spin. As a wave function, the "spin" is in a superposition of all directions.

See, the problem with spin is that it is one of the first "properties" one stumbles upon while studying quantum mechanics, which does not have a classical analogue. It is a property of the particle, which follows the same algebra as angular momentum, though it is different from it. The arrow we use, or the image of an electron "spinning" around itself, is just demonstrative - spin is not due to electrons moving around themselves.

Now, since the spin of an electron can take one of two possible values (spin = +1/2, spin = -1/2), we use the words "up" (+1/2) and "down" (-1/2) to be able to tell the two values apart (again, the electron does not have an "up arrow" on its head, it's just a way for physicists to communicate on common grounds). So, what happens when you get a system of two electrons? Each electron has a spin of its own, so when you study their system you are going to see one of the following possibilities:

1) Both spin up
2) Both spin down
3) One with spin up and one with spin down

Now, let's do something different. Instead of looking at electrons one by one, let's study their system first. I'm not sure if you have covered that part yet, but let's just say that a system that consists of two electrons can either have a total of spin = 0 or spin = 1 (you'll see in the future why, if you haven't already).

Spin = 0 is nothing but the so called "singlet" case, because there is only one way of "combining" the electrons' spins in such a way that gives a total of spin = 0 for the system.

But spin = 1? That's a different story. In this case, there are three different ways of combining electrons into making a spin = 1 system. This is why they call it "the triplet".

I'm not sure I helped you in any way, but I'd advise you to search online for angular momentum/spin coupling and Clebsch-Gordan coefficients.