It's such a broad term that you're likely to get a different answer from everyone you ask

But basically, it's the left. Ideas to benefit the common people first, mostly

American socialism has many major and key differences compared to the English, French, Russian, Chinese, Cuban or even the original Marxian socialism systems. Every country has a different interpretation but there are some common points.

The base idea of the thing, is as DeadSpark said, helping the lower class citizens. Socialism recognizes that citizens can be divided in different sociology-professional categories, or class. And that the lower classes (workers, proletariat etc) are in short exploited by the ones at the top in a inhuman way, and that society would greatly benefit from having these people not wallow in misery.

So the general idea is at least to help the poorest part of the population of said country. They do that by growing the public sector: developing public institutions, healthcare, schools, more public sector jobs etc. They also provide more monetary aids or increase the minimum salary, and create laws regulating work conditions for to the benefit of workers.

Of course this requires money, and while some systems are a lot more extreme than others, it always come from taxes, targeting more specifically the higher classes of society. So rich people and shareholders get less gross personal profit (money invested in companies are often left untouched), but that money is now redistributed between citizens. Only to an extent of course, this isn't communism in which the concept of property itself is questioned.