That term means beneath the skin and refers to the connective tissues and adipose tissues that are between the skin and above the muscles. Other terms that mean the same thing are hypodermis and superficial fascia.
You would tell the patient first that it doesn't and won't cause too much pain. Second, you tell the patient the definition, which is 'located or placed just beneath the skin'. By telling the patient...
intravenous means medication is delivered into a vein, ie into the blook subcutaneous means that meds are injected into the muscles or just below the skin