You can use @framer/motion package that allows you easily animate elements.

const menuVariants = {
    open: {
      opacity: 1,
      x: 0,
    },
    closed: {
      opacity: 0,
      x: '-100%',
    },
  }

Animations can be changed however you want according to @framer/motion docs.

And attach variants to your <MobileMenu /> component.

function MobileMenu({isMenuOpen}) {
  return (
    <motion.div animate={isMenuOpen ? 'open' : 'closed'}
    variants={menuVariants}> className="block md:hidden px-4 py-3 text-white w-full bg-gray-800 border-t border-opacity-70 border-slate-700">
      <div className="flex items-center mb-3 pb-3 border-b border-slate-700">
        <img
          src="https://africaprime.com/wp-content/uploads/2020/04/ElonMusk.jpg"
          className="rounded-full w-8 h-8 cursor-pointer"
        />
        <h6 className="ml-5 cursor-pointer">Elon Musk</h6>
      </div>
      <div className="mobile-nav-icon">
        <ImHome size={20} />
        <h4 className="ml-5">Home</h4>
      </div>
      <div className="mobile-nav-icon">
        <HiUsers size={20} />
        <h4 className="ml-5">Friends</h4>
      </div>
      <div className="mobile-nav-icon">
        <CgProfile size={20} />
        <h4 className="ml-5">My Profile</h4>
      </div>
    </div>
  );
}

export default MobileMenu;

And you can pass isMenuOpen variable as a prop.

function Navbar() {
  const [mobileMenuOpen, setMobileMenuOpen] = useState(false);
  return (
    <>
      <nav className="flex justify-between items-center px-4 lg:px-8 py-3 bg-gray-900 text-white">
        {/* Mobile Menu Icon */}
        <div
          className="block md:hidden p-2 cursor-pointer rounded-full hover:bg-gray-700 transition-2"
          onClick={() => setMobileMenuOpen(!mobileMenuOpen)}
        >
          <FiMenu size={20} />
        </div>
      </nav>
      {/* Mobile Menu */}
      {mobileMenuOpen && <MobileMenu isMenuOpen={mobileMenuOpen}/>}
    </>
  );
}

export default Navbar;