We often use "one" to substitute for "a person" or "he or she". That's true for this sentence, too.
"One cannot communicate" is grammatically correct alone as a simple sentence. However, some more information would help it make sense. It's probably part of a larger sentence, like:
When asleep, one cannot communicate.
One cannot communicate complex ideas to babies.
In other words, When a person is asleep, he or she cannot communicate. Or, for the second sentence, A person cannot communicate complex ideas to babies.
Sometimes, people use the word "you" for the same purpose. Both "you" and "one" can be used as what we call generic pronouns. In some situations, you can use either (or--"one can use either"! See?). However, "one" is more formal than "you", so I recommend using "one" in things like school papers and "you" in casual conversation.
If you understand how "one" is used, maybe you want to know the meaning of "communicate". I recommend that you use an English Learner's Dictionary to help find definitions in simple English. For example, Merriam-Webster's Learner's Dictionary provides 3 main entries for "communicate":
1 : to give information about (something) to someone by speaking, writing, moving your hands, etc. [+ obj]
2 : to get someone to understand your thoughts or feelings [no obj]
3 [+ obj] medical : to pass (a disease) from one person or animal to another
In all 3, the main idea is exchange, or sharing.
If we put all that together, we can understand that depending on the context, another way to say "one cannot communicate" might be "a person cannot get someone to understand his or her thoughts or feelings" or "you cannot give information to someone else."
The expression "one cannot communicate" is a saying that is figurative and classified as an idiom by some sources (idioms are sayings that have a figurative meaning that is different from their literal meaning and are broadly understood in a given culture). It means literally that an individual, let's say "you," cannot find a way to get another individual, let's say "her," to understand what you are saying or writing or otherwise expressing. A paraphrase of "one cannot communicate" might be: You speak your thoughts as well and clearly as you can, yet she does not understand what you mean. Or, more simply, you might say, "one cannot communicate."
"Communicate" in this figurative expression might also be seen as a metonymy that is a "catch word" that stands in for a more complex idea. The classic example of metonymy is "White House," which is a catch phrase (well known and easily recognized word or phrase) that stands in for the more complex idea defining the U.S. President: The President is the Chief Executive Officer and Commander in Chief of American government and military forces and has power to veto Congress. This complex idea can be and is expressed with the metonymy "White House": The White House defies Congress and vetoes the Bill.
In the same way, "communicate" might be seen as a metonymy for the idea that you try and try and try but you cannot find a way to make what you say understood: You cannot communicate. One (some unidentified person, perhaps yourself) cannot communicate.