Anyone can explain in the simplest form what are these SEO terms?

There is no such thing as do follow. I hate that word.
It's nonsense. What most people mean, is that it is a link
without a "nofollow." But that makes no sense. Google is
under no obligation to follow or count a link. But it's the only
links that google will count, if they actually count it.
Do follow is nonsense.

Nofollow will not count for anything positive. It was invented by google
to combat spam, letting webmasters put nofollow on links that
are untrusted. They do not count for PR, but can still split it.

It has been a big, fat, failure. People have morphed nofollow into
a bunch of nonsense, like hiding stuff and not indexing. That
is just insane, as nofollow is meaningless in those regards.

There is no reason to actively get nofollow links. They are
meaningless for SEO. There are some level of nofollow that
are not looked upon as spam, untrusted, or other. That would
be things like twitter, FB, etc. Those get nofollowed so people
cannot abuse it. Big difference between a nofollow link on
twitter and a nofollow link on your website, or someone elses
website to yours. A link on a website with a nofollow to you,
could mean that you are a spammer.

Nofollow does not mean not seen or noted by google, and
your page could get indexed by other means.

Nofollow has nothing good for SEO. Anyone who says it does,
is clueless.

I can only assume this thread was started as joke.

Paul