In the military sense, and relating to the United States Armed Forces, the rank of Captain holds different levels of importance and seniority depending on the branch of service and in what context.
Army, Air Force, and Marines
In the US Army, Air Force, and Marine Corps an officer holding the title of Captain is an O-3 on the pay scales (the third from lowest officer in pay grade). It is thus the third highest rank in the officer rank chart. A Captain is the equivalent of a Lieutenant in the United States Navy and Coast Guard. Captain in the Army, AF, and Marines is still considered a "Company Grade Officer".
At this point in their career, a Captain will generally be given a command position of a Company Commander or a similar appointment. This is usually the highlight of the career for most 4 or 6 year officers. A Captain is above both of the Lieutenant ranks, but below a Major. The insignia for a Captain in these branches is two parellel rectangular bars (two first lieutenant bars). The official Army abbreviation for Captain is CPT, while the Air Force and Marines officially abbreviate the rank as Cpt. (the capitalization and punctuation matters).
In the United States Navy, it's slightly different. The Captain is the commander of a Naval warship. If the commanding officer of a ship is a Lieutenant Commander he is still referred to as "Captain".
The Navy also has the rank of Captain. However, the rank is much higher than the rank of Captain in the other branches. The Naval Captain is equivalent to a Colonel in the Army, Air Force or Marine Corps. The naval Captain is an O-6 on the pay scales. Generally the top ranking officer of a Naval ship will indeed be a Captain in rank and position. The rank of Captain, being equivalent to a Colonel of the other branches wears the same insignia, an Eagle with spread wings perched on a branch in certain uniforms (such as khakis), or three bold, gold stripes on the sleeves of his dress uniforms.