Blow-dry (or blow dry or blowdry) is prevalently defined as follows:
To dry and usually style hair while drying it with a hand-held hot air blowing hair-dryer (blow-dryer) or Blow-comb.
Blow-dry as a noun is the above as the actual method of styling, removing moisture from hair and act of Blow-drying.
Related to Blow-Dry as a noun are: Blow-Drys or Blow-Dries (plural).
Related to the verb To Blow-Dry are: Blow-drying (Gerund) and Blow-dried (past participle)
Example: European Blow Dry (European based technique of blow-drying faster and better, also resulting in longer lasting effects.
The European Blow Dry technique is the latest for hair stylists and is a blend of techniques involving a blow-dryer and used in Europe for blow-drying, while styling, hair. Once blow-dried, hair can stay styled even for 4-5 days.
More for marketing reasons than linguistic, blow-drys are also called blow-outs, as a different, marketable, exotic and exciting way of referring to the same method of drying and styling hair.
Example: Brazilian blow-out.
In a sentence: In many countries Brazilian blow-outs are illegal on health and safety grounds.
The correct form for blow-dry is with a dash, however, blow dry without dash is used often and so is blowdry.
The plural can be blow-dries or blow-drys, and it’s also the third-person singular simple present indicative form.