What's the difference?
A monolingual dictionary is an English-English dictionary.
A bilingual dictionary translates between English and another language.
The best language learners use both to their best advantages.
Which should I use for writing?
Many people use both. If you do not know a particular word in English, use a bilingual dictionary first. However, to use the English word correctly, you may need to look it up in a monolingual (English-English) dictionary.
The advantage of monolingual dictionaries is that they usually provide much more information about the word - for example, if it is formal or informal, positive or negative in attitude, dated or in frequent use today. Best of all, a monolingual dictionary will often show you how to use the word in a sentence. For example, it might tell you useful collocations (=words that go together) and the grammatical structure that you need to follow.
As, a result, looking up a word in a monolingual dictionary can greatly help your writing even if you already know the meaning of the word.
What about for reading?
For reading, a bilingual dictionary is quicker, but a monolingual dictionary helps you to keep your concentration in English.
English-English (Monolingual) Dictionaries
International (Bilingual) Dictionaries