The short, glib answer is that if you have to ask why you would want to pay for a dictionary, then you aren't the kind of person who needs to pay for a dictionary.
The long answer is that good dictionaries, such as American Heritage Dictionary, the Shorter Oxford English Dictionary, and the OED itself, are produced by scholars and experts, guided by editorial panels comprised of scholars and experts, require a great deal of work to produce (the first edition of the OED took something like 71 years to complete!), and contain more data (i.e., more words and more definitions per word) and generally higher quality data than free dictionaries. You're probably willing to pay $50 for software that solves your problems, because you probably make software yourself, and you know that it costs money to create software; an analogy can be made here. But if a barebones dictionary works for you, then it works for you, and don't worry about it.
So what is a good dictionary? Here's a tentative answer. A good dictionary provides pithy, useful definitions that reflect the words' differing meanings over time and differing contexts. Most good dictionaries also provide style and usage guidelines (e.g., "When should I use 'lie' and when should I use 'lay'?"), and a good dictionary will also provide a word's etymology. Many free dictionary apps use data from WordNet, which is an amazing resource, but its focus is on tagging words with taxonomic properties (sorry, a better phrase isn't coming to me right now) and defining the relationships between those words, all of which is very useful for general linguistics and NLP research. The quality of the definitions fall short, and you should be able to confirm this by comparing just about any WordNet definition to a definition from a good dictionary at your library.
I was hoping to find a better example, but to give yourself an idea of the research problems that can be solved with a good dictionary, consider reading this brief student's guide to using the OED:
For those living in the UK, it's probable that you can access the online master OED through your local council's library web site, using your ridiculously long library card number as username.
It's probably a bit much, but I'm going to go ahead and say...
It seems somehow fitting that a company which feels entitled to $50 for a dictionary app would also feel entitled to commandeer a supposed pirate's Twitter account for public embarrassment or do something equally smug [1].
