These days many use the term left-wing or leftist to refer, simply, to anyone who is not conservative. Also these terms (like the term right-wing) are often used to mean extreme and/or anti-American. Those who call themselves left-wing or leftist, on the other hand, understand conservatives and liberals to be alike in foolishly hanging on to the idea that capitalist systems can lead to fair outcomes without the government going so far as to interfere with property rights to reduce inequality, ensure robust democratic processes, and protect the environment. Specifically, leftists believe that capitalist market economies (1) have always depended on government action and force and (2) necessarily put heavy pressure on most investors to take steps bad for all in the long run: for example to gradually destroy the environment, to sell harmful products, and to pay workers too poorly to keep the economy going. Furthermore, leftists see concentration of wealth in the hands of "the 1%" as an obstacle to the further democratization of society.  Many leftists see liberals as foolish in thinking that government assistance and spending programs can "fix" capitalism, making it fair for all.  On the other hand, many leftists appreciate free-market libertarians as honest opponents, but think more traditional conservatives (e.g. establishment Republicans) foolish as well, for ostensibly advocating free market capitalism and promoting the interests of small businesses, while at the same time supporting the kind of Big Government-Big Business collusion supporting American military overreach abroad and cronyism at home.  

What do leftists want?  In a word:  "democracy", or, more specifically, "economic democracy", in which democratic principles are extended beyond the formal political sphere and are applied to the economic sphere as well.  What does this actually look like in practice?     Some leftists still speak of the need to "abolish capitalism" entirely (since they believe that capitalism is inherently anti-democratic in that it concentrates economic power--and thus political power--in relatively few hands).  However, because difficult questions face the project of completely replacing capitalism with some form of socialism  (How would goods and services be produced? How would resources be allocated? How would the concept of "community ownership" be operationalized?), various degrees and methods of "socialization" (i.e. democratization) are proposed by different leftists.  Some want democratically-accountable government to own some of the big businesses.  Some want all businesses to be worker-owned and democratically managed. Some want community panels to be able to overrule private corporate investment decisions. Some want capital investment to be guided by parameters set by the community (e.g. in the form of community-based credit unions or publically owned and operated State Banks).   Most want a single-payer health system.  

It is perhaps understandable that some people consider leftists to be "Anti- American." After all, to many, to be "American" is to endorse 'free enterprise" and leftists are critical of free enterprise;  but many leftists see themselves as pursuing the fulfillment of the fundamental American principle of "all people are created equal".  The general principle guiding leftists is in fact the idea that economic power determines political power, so that if we want to "form a more perfect union" and provide for those social conditions most supportive of the inalienable rights of all people to "life, liberty and the pursuit of happiness", economic power itself must be decentralized and democratized.