The connotation of a word refers to a different meaning a word has, it's a deeper or further assosiation this word suggests. This means that it exceeds it's literal meaning. The connotation of a word involves an idea or feeling. It differentiates from the denotation of the word, it's literal meaning, the one found in a dictionary.
An example is: the word "lion". It's literal meaning is "a large wild animal of the cat family with yellowish-brown fur that lives in Africa and southern Asia".
But the connotation of "lion" can refer to someone who is brave, very strong, or majestic.
Mount Everest attracted the author because it is the highest, the mightiest and has defied many previous attempts. It takes the last ounce of one's energy.