Oh, I wish I knew more about the context of your question! It would make such a difference as to whether you have gotten this quotation from inside of a history textbook, out of a novel, out of a magazine, or out of someone's everyday speech!
I am sure that the word "liberty," which of course generally means "freedom", is what is confusing to you. If someone speaks of "a particular liberty" it means a specific kind of freedom. There is SO much freedom in the United States (some say to our detriment!) that it would be impossible to list ALL of the "particular liberties" that we can have. For example, there is the "formal" liberty that is the "Freedom of Speech" while there is the "informal" liberty of being able to walk down the street with mismatched shoes and socks.
Freedom of Speech is the liberty for all US Citizens to be able to express their opinions with words (out loud or in print) despite what the opinion is (even if it is against the government!). Freedom to Bear Arms is the liberty of a US citizen to be able to obtain a deadly weapon in order to defend himself or herself. Freedom to Congregate is the liberty for US citizens to gather, no matter what the reason. There are many other more "formal" liberties, but these are just a few. Perhaps these are some of the "particular" liberties that you mean?
In conclusion, let me say that it is also "a particular liberty" that I can work via the eNotes company and earn money for myself. So, in a sense, me answering this question for you PROVES the answer. How blessed I am to live in a country with such freedom, ... with such "liberty."
Noelle Thompson has given you a great list of some of the particular freedoms Americans enjoy, so there is no need to comment further on that. However, the way the assignment is framed, there seems to be an implication that you are meant to discuss a freedom that people in other countries are not fortunate enough to have. This would involve a little research, I would think. What countries do not have freedom of speech or freedom of assembly, for example? I assure you there are countries that do not. On this very day, all Americans now have the freedom to marry, which many countries do not provide. Freedom of the press and the right to bear arms are other freedoms not afforded to those in some other countries. Do a little checking, so you can appreciate all the wonderful freedoms we do have.
When I encounter a confusing phrase, I always try to break it down into smaller, more digestible pieces and then look up definitions as I need them.
"a particular liberty that US citizens enjoy"
"particular": this word is used to identify a single one out of a group
"liberty": the word I most closely associate with liberty is freedom
-->Therefore, "a particular liberty" just means a specific freedom (out of the many possible, like freedom of speech, freedom of religion, etc.)
"US citizens": relatively self-explanatory; strictly speaking, think of a citizen as a legally recognized "member" of the United States
"enjoy": here, the enjoy is used in reference to the "particular liberty", and since liberty/freedom have such positive connotations in our society, it makes sense that having a specific freedom can also be described as enjoying it
-->Putting everything together, the phrase "a particular liberty that US citizens enjoy" can be simplified as a specific freedom that US citizens have. Some freedoms that may help start your train of thought for the essay include the ones I discussed earlier in the response (freedom of speech, freedom of religion), as well as the other ones included in the Bill of Rights, for example.
Hope this helps!
Thank you. That did help. I guess i should have elaborated on what i was asking. I am taking an Ethics class and we were asked to write about a particular liberty that US citizens enjoy. I was just having a hard time with understanding what, exactly, that was.