> Does this mean I cannot use openssl in my gpl-2.0-only program?
Correct.
> How does that work?
The GPL 2.0 and Apache-2.0 licenses contain terms which are incompatible with each other.
> Doesn't gpl-2.0-later imply that I can also take the code and use it in gpl-2.0-only?
Yes, in that case you can choose whether you use the code subject to the gpl 2.0, 3.0 or any later version. If you combine that code with some gpl-2.0-only code then you're choosing to use the first code under 2.0, and the combined work is then gpl-2.0-only.
> Is there some tldr on this topic somewhere? I'm not good with these legal things to ELI5 would be nice :/
The GNU project maintains a list of licenses and some comments about them, and conveniently categorizes them according to their GPL compatibility.
https://www.gnu.org/licenses/license-list.html
See also the chart at http://gplv3.fsf.org/dd3-faq for compatibility between the different GPL versions and variants.