Simple Grid Snapper script to show how the Grid component can be used to align GameObjects along the cells of a Grid.

GridSnapper.cs

/// <summary>
/// - Make sure you have a Grid GameObject (any GameObject with a Grid component attached to it) in the scene.
/// - Attach this script to the GameObject you wanna snap to the Grid. Then drag and drop the Grid 
/// GameObject into the AttachedGrid field to create a reference to the Grid component attached to it.
/// - Enter Play Mode, and then every time you hit the Space key, this GameObject will move 1 unit
/// down along the Y axis, while remaining snapped to the Grid.
/// </summary>

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

public class GridSnapper : MonoBehaviour {

	public Grid AttachedGrid;

	// Use this for initialization
	void Start () {
		
	}
	
	// Update is called once per frame
	void Update () 
	{
		if(Input.GetKeyDown(KeyCode.Space))
		{
			// Calculate the cell position on a Grid that is closest to this GameObjects world position.
			Vector3Int TileCellPosition = AttachedGrid.WorldToCell(transform.position);
			
			TileCellPosition.y -= 1; // Move 1 unit down on the Y axis.
			
			// Convert the cell position into a position in World Space.
			Vector3 TargetPosition = AttachedGrid.CellToWorld(TileCellPosition); 

			// Add (AttachedGrid.cellSize.x/2) and (AttachedGrid.cellSize.y/2) on the X and Y axes so 
			// that the GameObject is centered in the cell, regardless of cell size.
			TargetPosition.x += (AttachedGrid.cellSize.x/2);
			TargetPosition.y += (AttachedGrid.cellSize.y/2);

			// Apply TargetPosition to this GameObject's position.
			transform.position = TargetPosition;
		}
	}
}