Wet clothes are spread out over the laundry line to get them dried up quickly. More surface area of water is exposed to the air and this speeds up the rate of evaporation and clothes are dried up quickly.
With an increase in temperature, the particles of liquid at surface require kinetic energy to overcome the force of attraction and escape in the air quickly. Hence, the increase in temperature increases the rate of evaporation.
In the rainy season, the relative humidity (moisture content in air) is high, and so more water cannot be held in the atmosphere. Therefore, the moisture from clothes cannot be absorbed in the air. Hence it takes longer to dry clothes in the rainy season.