Just had a pft and was told that I have small airway disease showing obstructions in my small airways. What does that mean? I.E. Asthma or COPD or something else? Born at 27.5 weeks and on vent as baby.

Asthma. The most typical reason for "small airway" disease in someone young is asthma or viral infection. Prematures can also have chronic lung disease and it is possible for those changes to be permanent. If you have asthma (and probably even if you have chronic lung disease from being premature) you can improve your lung function with appropriate therapy. Pulmonary anti-inflammatory therapies are key.
Still controversial. Small airway is considered the primary defect in asthma but one cannot diagnose the presence of asthma by small airway obstruction alone. In fact it is often present in seemingly well controlled asthma. I presume that your fvc and fev-1 were normal and thus would not lose sleep over it. COPD is also not diagnosed by this measure.
Workup/Mgt. Many former premature infants continue to have airway problems even later in life. The exact nature of the problem may be related to reversible airways disease. COPD is less likely since you have no smoking history. I would recommend albuterol before and after spirometry and an evaluation for allergic disease as well.
Possible. Small airways disease is those > 2mm, or the terminal airways. They can be affected in different conditions, including asthma and copd. Inflammation probably plays a major role in this condition, so using anti-inflammatory medications (usually steroids) makes sense. Inhaled small particle steroids are more effective than larger particle. See your provider or a pulmonologist for more info.