How do you explain a distinct query in MongoDB?

As of Mongo 3.2, you can do:

db.test3.explain().distinct("id", {key: "value"})

https://docs.mongodb.org/manual/reference/method/db.collection.explain/

You cannot use explain with the distinct as per this mongodb jira ticket. Instead you can use runCommand and verify the stats,which is kinda similar to explain()

 db.runCommand({ distinct: 'test3',key:'id',query:{key:"value"}})

In the above query test3 is collection name, key is a field name you want to apply distinct and finally if you wanted to specify any filters use query.

Check the samples

> db.runCommand({ distinct: 'items',key:'name',query:{offered:true}})
{
    "values" : [
        "test flat",
        "Another aston martin",
        "super luxury villa",
        "Aston martin vanquish y for sale",
        "Super car",
        "Test item",
        "another sports car",
        "super car"
    ],
    "stats" : {
        "n" : 8,
        "nscanned" : 10,
        "nscannedObjects" : 10,
        "timems" : 45,
        "cursor" : "BasicCursor"
    },
    "ok" : 1
}
> db.runCommand({ distinct: 'items',key:'name',query:{offered:false}})
{
    "values" : [
        "yamaha",
        "Test item"
    ],
    "stats" : {
        "n" : 2,
        "nscanned" : 10,
        "nscannedObjects" : 10,
        "timems" : 0,
        "cursor" : "BasicCursor"
    },
    "ok" : 1
}