What Are Those Stripes and Bars? explains the insignias worn by different ranks in the U.S. military. Enlisted men (and women) have chevrons:
Chevrons. Worn by most enlisted personnel in every military service branch, the chevron is composed of V-shaped stripes. The use of these insignia can be traced to feudal days, when knights were awarded chevrons for capturing a castle or other building. This may explain the chevron’s ‘roofed’ appearance and French root of word meaning ‘roof.’ In heraldry, the chevron denoted those who were head of a clan — or, ‘top of the house.’
The (fairly generic) bars, eagles, and stars of officers all seem pretty straightforward, by why oak leaves?
Oak leaves. Officers at the O-4 and O-5 pay grades wear a gold oak leaf and silver oak leaf, respectively. The true origin of oak leaf use across the service branches is a mystery, though it could have been borrowed from the Navy. The Navy took much of its tradition from the British, and in 1650, King Charles II escaped his enemies by hiding in an oak tree. When the insignia is the same — specifically with bars and oak leaves — the junior rank is gold and the more senior rank is silver.