SPDY is a new protocol created by Google and given to the Apache Foundation which allows faster Web traffic under SSL. Apache 2.4 is SPDY capable but its module is not included in Ubuntu 14.04 LTS Server. Here are some instructions that allow to get, install and enable SPDY feature foe Apache 2.4 under Ubuntu 14.04.

Get the third party Apache 2.4 module, extract and install it:
cd /usr/local/
tar zxf mod_spdy.tar.gz
cd /usr/lib/apache2/modules
mv /usr/local/mod-spdy/mod-spdy/src/mod_ssl.so .
mv /usr/local/mod-spdy/mod-spdy/src/out/Release/libmod_spdy.so mod_spdy.so
echo "LoadModule spdy_module /usr/lib/apache2/modules/mod_spdy.so" | sudo tee /etc/apache2/mods-available/spdy.load
echo "SpdyEnabled on" | sudo tee /etc/apache2/mods-available/spdy.conf
a2enmod spdy
service apache2 restart

In case you get the error message in log file eg:
...... [core:notice] [pid 7842:tid 140724740487067] AH00052: child pid 8025 exit signal Segmentation fault (11)
Then that means that you are using a version of the MPM that is not compatible with SPDY module. You might need to change to the thread-stable mpm_prefork as follows:
a2dismod mpm_event
a2enmod mpm_prefork
service apache2 restart

Test your sites for SPDY protocol: