Merriam-Webster says "speech expressing hatred of a particular group of people".
The
Legal Dictionary says "Speech that is intended to offend, insult, intimidate, or threaten an individual or group based on a trait or attribute, such as sexual orientation, religion, color, gender, or disability."
Cambridge says "public speech that expresses hate or encourages violence towards a person or group based on something such as race, religion, sex, or sexual orientation (= the fact of being gay, etc.)"
Brittanica says "speech or expression that denigrates a person or persons on the basis of (alleged) membership in a social group identified by attributes such as race, ethnicity, gender, sexual orientation, religion, age, physical or mental disability, and others."
The issue of whether such speech is protected by the Constitution is a difficult one. It's been found by SCOTUS that various forms of speech are
not protected (the classic example is yelling 'Fire!' in a crowded theatre - we do not have the Constitutional right to do so), so protected 'free speech' does not automatically include any/every kind of speech.
However, SCOTUS has also found that 'hate speech' does not automatically get the same exemption - that is, that the right to 'hate speech'
is protected, and we have the Constitutional right to it.
Wikipedia has a pretty good page specifically on hate speech in the US and how it has been viewed.
For myself, I am a huge free speech advocate. I think hate speech should
not be restricted. I think the only types of speech (and I include in that other methods of expression, such as in writing, on t-shirts, placards, etc.) which should be restricted are those for which it can be demonstrated that harm to people (other than the speaker) is virtually inevitable (such as yelling 'Fire!' in a crowded theatre).
Another complex area is the idea of private retribution. If a person publishes a statement (online, in a newspaper, wherever) that qualifies as hate speech, denigrating a particular group (doesn't matter which one), that statement is protected by the Constitution, and they will suffer no legal repurcussions for it. However, people can and do act against that person by (for example) firing them, boycotting their business, etc. Should we be doing that? Should we be encouraging others to do that? Should we be alerting others to that person's opinion, so they can take whatever action they deem appropriate?
I think these questions are difficult ones. If I found out that a particular business was owned by people who have opinions in accord with hate speech, I would go out of my way to not patronise that business. In fact, I do so in regard to a couple of businesses. I don't want my money to go to such people.
But is it right for me to organise a boycott of those businesses, with the aim of preventing others' money going to them? Is it right for me to tell others (here I'm meaning friends, people I personally know) of the opinions of those owners, so that they are aware and can not patronise them, if they choose?
Is there really a difference between me telling a friend that <insert business> is owned by people who think <insert viewpoint I find objectionable>, so that that friend can take their business elsewhere, if they choose, and me taking out an add in the newspaper telling every reader the same thing? I'm not sure.
