Really basic example of a draggable shape in the Love2D framework

draggable.lua

local box = {x=10,y=10,w=50,h=80}
local mouseButton = 1

function love.load()
  love.graphics.setBackgroundColor(255,255,255)
  love.graphics.setColor(225,62,62)
end

function love.draw()
  love.graphics.rectangle("fill", box.x, box.y, box.w, box.h)
end

function love.mousepressed(x, y, button, istouch)
  if button ~= mouseButton then return end
  local dx = x - box.x
  local dy = y - box.y
  if dx >= 0 and dx <= box.w and dy >= 0 and dy <= box.h then
    love.update = function()
      if not love.mouse.isDown(mouseButton) then
        love.update = nil
        return
      end
      local x,y = love.mouse.getPosition()
      box.x = x - dx
      box.y = y - dy
    end
  end
end