ah.test.js

import chai, { expect } from 'chai';
import { describe, it } from 'mocha';
import chaiHttp from 'chai-http';

chai.use(chaiHttp);
chai.should();

const newArticle = {
  title: 'Design patterns',
  body: 'There are several design patterns e.g: MVC pattern',
  description: 'List of most popular design patterns used in Javascript'
};

describe('Test cases for Authors Haven app', () => {
  it('POST /articles/', (done) => {
    chai.request(app)
      .post('/api/articles')
      .send(newArticle)
      .end((err, res) => {
        res.should.have.status(201);
        res.body.should.be.a('object');
        res.body.article.should.be.a('object');
        res.body.article.id.should.be.a('number');
        res.body.article.title.should.equal('Design patterns');
        res.body.article.body.should.equal('There are several design patterns e.g: MVC pattern');
        res.body.article.body.should.equal('List of most popular design patterns used in Javascript');
        done();
      });
  });
})

Instead of hardcoding the expected values like you have done, to be on the safe side, you could use a reference to the original data you sent to the server i.e. res.body.article.title.should.equal('Design patterns') could be rewritten as res.body.article.title.should.equal(newArticle.title). This assertion as you have written it would fail if a single space or a character is mistakenly included in the hardcoded strings.
But the code is neatly written and clear