What are fossils? Describe briefly two methods of determining the age of fossils.

Fossils are defined as the remnants or traces of dead plants and animals that died more than 10,000 years ago.

Fossils are mainly formed when plants and animals die in watery environments or buried in mud and silt. Soft tissues decompose quickly leaving the hard bones or shells afterward.  As time passes, sediment accumulates over it and hardens to form rock. For example, archeopteryx.

The age of fossils is determined using the absolute dating method and relative dating method.

In the absolute dating method, a scientist can measure the ratio of remaining Carbon-14 to the unchanged Carbon-12 to see how long it has been since the material's source died. Advancing technology has allowed radiocarbon dating to become accurate within just a few decades in many cases. 

While, in the relative dating method, the age of fossils is determined by comparing them with the other fossils or rocks whose age is pre-determined or recorded.