Nodejs:Array data not added in mongodb

Since you marked the properties of educationinfo as required, you need to provide them when you create an instance of Profile. If you don't want to do that you need to remove the required property from those properties that you won't be supplying on instance creation like below:

const mongoose = require('mongoose');

const ProfileSchema = mongoose.Schema({
    educationinfo: [{
        universityname:
        {
            type: String,
            required: true
        },
        degree:
        {
            type: String,
            required: true
        },
        coursecompletionyear:
        {
            type: String
        },
        collegename:
        {
            type: String
        },
        specialization:
        {
            type: String
        },
        marks:
        {
            type: String
        },
        courselevel:
        {
            type: String
        }
    }]
});

const Profile = module.exports = mongoose.model('Profile', ProfileSchema);

After making those changes, you need to make one more change in your POST route, change $educationinfo to educationinfo

router.post('/addprofiledetails', function(req, res, next) {
  const newProfile = new Profile({
    educationinfo:[{
        universityname: req.body.universityname,
        degree: req.body.degree
    }]
  });
  newProfile.save((err, profile) => {
    if (err) {
       res.json({ msg: 'Failded to add profiledetails' });
    } else {
       res.json({ msg: 'successfully add profile details' });
    }
  });
});

The data you insert is incomplete. The properties in your schema marked as required: true need to be inserted aswell. Because you do not meet the schema requirements, it is failing.