The basic difference between the percentage and percentile is that percentage is based on absolute marks and it indicates your absolute marks out of Hundred when your maximum marks is not hundred. but in case of percentile it indicates your position merit list that is it a relative phenomena and explain the relative position among the candidates appeared in the exam.

suppose there are 200 candidates and the exam and maximum marks for the exam is 500 and if you score 300 marks in the exam then your percentage would be 60 but if you are the highest scorer of the exam it is 300 marks is the highest then you are percentile score will be hundred.

Hiiiii

I would suggest you to please mention for which exam are your asking because percentile is calculated differently for different exams. For some exam is is calculated by total number of students qualifying and in some it is calculated by the higher marks.So to get a better answer please mention the exam.
A general difference is provided here.
A percentage is simply a representation of a proportion out of 100. To say three out of every six is the same as to say fifty out of every hundred, in other words fifty percent 
A percentile is a statistical measure of distribution. For a given set of data, it is the level below which a certain percentage of the data falls. In graphic terms, it represents the area under the curve of a distribution.
For example, if you score in the 72nd percentile on an exam, it means you scored higher than 72 percent of all the people who took the same exam— regardless of what your actual score was.
If a baby is in the 28th percentile for length, it means she is longer than 28 percent of all comparable babies i.e babies of certain age.

Hope this helps.
Thanks!