The molecular structure of Ibuprofen consists of a phenyl ring with an isobutyl group attached to one side and a propanoic acid group attached to the opposite side. The name "Ibuprofen" comes from its old chemical structure name: iso-butyl-propanoic-phenolic acid. Using the modern naming system (IUPAC), the molecule is now called (RS)-2-(4-(2-methylpropyl) phenyl) propanoic acid. I have attached several image files with the structure of ibuprofen, including one where I labeled the functional groups.

Ibuprofen is a common analgesic, a medicine used to relieve pain.Similar drugs include 2-acetoxybenzoic acid (also know asacetylsalicylic acid, or most commonly aspirin) and N-(4-hydroxyphenyl) acetamide (also know as paracetamol, acetominophen, or by the brand name Tylenol). All three of these drugs share the same core molecular structure of a phenyl ring (a ring made of 6 carbons) with two functional groups attached. The difference is that each molecule has different functional groups in different positions on the ring.

Ibuprofen is an extremely important drug world-wide. The World Health Organization (WHO), the United Nations public health agency, lists iton their core list of essential medicines along with acetylsalicylic acid and paracetamol (aspirin and Tylenol). The core list of essential medicines "is a list of the minimum medicine needs for a basic health-care system, listing the most efficacious, safe and cost-effective medicines for priority conditions".

References:
Wikipedia
Ibuprofen
Aspirin
Acetaminophen
Images are from Wikipedia.
WHO Website
selection_medicines