Partner had a massive headache then nose was running a yellow liquid and now headache is gone.. what does this mean?

Sinus drainage: My guess is that there was sufficient pressure in the sinus cavities to cause pain. Then something caused a release (position, food, fluid intake, activity, etc.) and there was drainage that removed enough pressure to lessen (stop) the pain.

Possibly sinus: Sinusitis is characterised by frontal headache, blocked, or runny nose, facial tenderness and possibly fever. It is usually viral and self limiting ... see http://patient.info/health/acute-sinusitis for more details. Simple analgesics such as Paracetamol or Ibuprofen are usually sufficient. See your Dr if unwell, or worsening pain

Snot: This sounds like pain from a build up of mucous in the sinuses (snot). The pressure from the build up of mucous can cause intense headaches but once the mucous clears the pain should resolve.