A word or phrase can have more than one "sense." Sense means roughly the same thing as "meaning." The "literal sense" is one possible kind of sense. The opposite of "literal" is "figurative."
For example, suppose I say "I am carrying a heavy weight."
Suppose I am an Olympic athlete competing in the hammer throw. The hammer weighs 16 kg. I am carrying a heavy weight in the literal sense. I am actually carrying a thing, and the thing I am carrying is a heavy weight.
Suppose that I am competing in swimming, and I am very worried and anxious because everybody expects me to win a gold medal and I am not sure that I will. Swimmers do not carry weights! I am not literally carrying a heavy weight. But I am carrying a heavy weight in the figurative sense. But, figuratively, I am carrying a weight. I am carrying the emotional weight of peoples' expectations.