Why 'apt-get install openssl' did not install last version of OpenSSL?

You should choose the version you want to install on the OpenSSL's site. It seems you want to install the 1.1.0. So, do as it follows.

wget https://www.openssl.org/source/openssl-1.1.0f.tar.gz
tar xzvf openssl-1.1.0f.tar.gz
cd openssl-1.1.0f
./config -Wl,--enable-new-dtags,-rpath,'$(LIBRPATH)'
make
sudo make install

openssl version -a

It is done. It is as simple as that. Good luck with it.

If you are using Ubuntu 18+, version 1.1.0 is now be available via apt.

You can also use apt list openssl to see what can be updated. And even throw in the -a modifier to show all versions available.