WiredTiger storage engine primarily offers the following benefits :
While updating a document, MongoDB acquires a write lock on the collection level. So, during this period your reads may be affected. In my opinion this is great if you expect less number of writes as compared to the reads. But what if you are building an app with more writes than reads or mixture of reads and writes? This is where WiredTiger can help you. WiredTiger engine offers document level locking which results in better concurrency.
Also WiredTiger by default uses Snappy compression algorithm which provides good balance between high compression ratio and low CPU overhead. There are also other algorithms that you can take advantage of depending on your requirements.
Check out this article to know what features WiredTiger brings to the table.
The default storage engine is MMAPv1. To switch to WiredTiger pass the flag --storageEngine wiredTiger.