What is the difference between concurrency and parallelism?
Examples are appreciated.
"Concurrent" is doing things -- anything -- at the same time. They could be different things, or the same thing. Despite the accepted answer, which is lacking, it's not about "appearing to be at the same time." It's really at the same time. You need multiple CPU cores, either using shared memory within one host, or distributed memory on different hosts, to run concurrent code. Pipelines of 3 distinct tasks that are concurrently running at the same time are an example: Task-level-2 has to wait for units completed by task-level-1, and task-level-3 has to wait for units of work completed by task-level-2. Another example is concurrency of 1-producer with 1-consumer; or many-producers and 1-consumer; readers and writers; et al.
"Parallel" is doing the same things at the same time. It is concurrent, but furthermore it is the same behavior happening at the same time, and most typically on different data. Matrix algebra can often be parallelized, because you have the same operation running repeatedly: For example the column sums of a matrix can all be computed at the same time using the same behavior (sum) but on different columns. It is a common strategy to partition (split up) the columns among available processor cores, so that you have close to the same quantity of work (number of columns) being handled by each processor core. Another way to split up the work is bag-of-tasks where the workers who finish their work go back to a manager who hands out the work and get more work dynamically until everything is done. Ticketing algorithm is another.
Not just numerical code can be parallelized. Files too often can be processed in parallel. In a natural language processing application, for each of the millions of document files, you may need to count the number of tokens in the document. This is parallel, because you are counting tokens, which is the same behavior, for every file.
In other words, parallelism is when same behavior is being performed concurrently. Concurrently means at the same time, but not necessarily the same behavior. Parallel is a particular kind of concurrency where the same thing is happening at the same time.
Terms for example will include atomic instructions, critical sections, mutual exclusion, spin-waiting, semaphores, monitors, barriers, message-passing, map-reduce, heart-beat, ring, ticketing algorithms, threads, MPI, OpenMP.
Gregory Andrews' work is a top textbook on it: Multithreaded, Parallel, and Distributed Programming.