The term Ashutosh means one who is easily pleased. Lord Shiva is called by this name since He is highly compassionate and merciful and does not discriminate between devas (gods), asuras (demons) and naras (humans) for granting the boons they ask for. There are several stories from mythology that highlight Shiva’s easily pleased nature.
Once the arrogant and proud Ravan, the demon ruler of Lanka and the villain in Ramayan was passing over the Hi9malayas in the sky. When he was about to cross over the Mount Kalias on which Shiva resides, Nandi Dev (the mighty bull god who is the guardian of Lord Shiva’s abodes) stopped him and said he cannot directly pass over the abode of Shiva and so he must only go around to move to the other side. Ravan’s ego could not digest being asked to take an alternative route. In all his arrogance, he insulted Nandi Dev and also said he can uproot the whole of the Himalayas with his mighty power.
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Ravan came down and put his hands below the Himalayan hills in an attempt the overthrow it. The entire region trembled as though it experienced strong tremors. Shiva in a playful way pressed his toe against the land below him and Ravan got trapped blow the mountain and wailed in agony unable to bear the weight pressing on him. A sage engaged in penance in that region advised Ravan to sing a song in praise of Lord Shiva which would please the Lord and win his grace. Ravan started plucking his own nerves to make a harp and started singing the glories of the Lord. The most merciful one at once got pacified and appeared in front of Ravan.
The Lord showered his mercy on Ravan and said he was highly pleased with Ravan’s song. Lord Shiva released Ravan from below the mountains and also granted a sword named Chandrahaas, which is unconquerable. However, Shiva also advised that if the sword was used for an unethical purpose, it would leave Ravan and reach Lord Shiva once again. Being forgiven and also granted a boon, Ravan praised the Lord for his mercy and moved forward with his voyage. In this story we see how Shiva is easily pleased to grant his boons to those who pray him.
If you remember the story of Ramayana, Ravan used this sword to kill the bird Jatayu who tried to stop Ravan when Ravan had abducted Mother Sita and carried with him. Since it was an unrighteous act for which he was not supposed to use the sword gifted by Shiva, the sword disappeared and reached Lord Shiva as per the caution made by Shiva earlier while gifting the sword to Ravan.
Now the point is, the story illustrates to point that Lord Shiva is highly merciful and granted bounteous boons even to Ravan who first intended to insult Lord Shiva. Therefore, the expression Ashutosh – the easily pleased one is a fitting title to describe Lord Shiva. There are hundreds of stories that highlight the merciful nature of Lord Shiva.