It means that you don't have to do the thing(s) you are "under no obligation" to do.
For example, someone wants to sell you something. They are willing to come to your home and demonstrate how their product works. If they tell you that you are "under no obligation" to buy it, it means that you don't have to buy it.
Of course they will try to convince you how good it is and that it will make your life much easier or enjoyable. They will try to persuade you to buy it, but you are free to say 'no thanks'. You don't have to buy it just because they took the trouble of coming to your home and giving you a free demonstration.
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