As a stative, it means (normally of things) 'to convey a certain feeling or sensation', as in
This beer feels cold.
As a dynamic (or 'action') verb, it means either (of a person) 'to experience a sensation', as in
I'm feeling sick.
(N.B. It is also often stative in this sense, thus I feel sick could be interchangeable with the above).
or (also of a person) 'to touch carefully, as if, for example, to determine the nature of something', as in
She was feeling the bag to see how heavy it was.