my character is going thru mesh but is staying on top of the grid

i have a downloaded a cat off the unity asset store and he cut thru mesh but stays on top of the grid but if i move him up he goes back down to the grid if i press play i have tried box collider, and i cant find any videos of that problem plz help

       @lambo24

i dont exactly have him moving yet but here is the code that is on him for his animations and i am also making him jump but that code has like one line of code so far

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class animationmove : MonoBehaviour
{
Animator anim;

// Use this for initialization
void Start ()
{
    anim = GetComponent<Animator> ();
}

// Update is called once per frame
void Update ()
{
    //handling the idle-looking-idle state change
    if (Input.GetKeyDown(KeyCode.L))
    {
        anim.SetInteger("state", 1);
    }
    if (Input.GetKeyUp(KeyCode.L))
    {
        anim.SetInteger("state", 0);
    }
    //handling the idle-running-idle state change
    if (Input.GetKeyDown(KeyCode.W))
    {
        anim.SetInteger("state", 7);
    }
    if (Input.GetKeyUp(KeyCode.W))
    {
        anim.SetInteger("state", 0);
    }
    //handling the idle-walking-idle state change
    if (Input.GetKeyDown(KeyCode.S))
    {
        anim.SetInteger("state", 2);
    }
    if (Input.GetKeyUp(KeyCode.S))
    {
        anim.SetInteger("state", 0);
    }
}

}

The cat and the mesh need colliders. Mesh Colliders are tricky, that could be your issue. Try it with both the cat and the floor having box colliders. Make sure the cat starts out completely above the floor and see if it can fall to it.