Any resume needs to follow some standard guidelines. The contact details of the person should be clearly written. Please recheck these details as a typing error could make you inaccessible for the company and, thus, prevent you from getting that coveted internship.
Your educational details, along with your grades/percentage should be clearly mentioned. Many companies have some criteria for the educational qualifications. If the internship requires a little basic knowledge of the subject your education might help them figure out your suitability for the job.
Your extra-curricular activities during school and college should be neatly arranged in your resume. Many people make a table in their resumes and organize their activities and achievements according to the year, or the class. A messy resume is bound to work against you. There are chances that the person reading your resume could miss out some piece of information, which would have enhanced your candidature and focus on the irrelevant part. Do not give information that is too old and, hence, irrelevant. The employers are unlikely to be interested in what you did in sixth grade.
Your resume could also contain a line or two explaining what you hope to gain from the internship you have applied for. Try to be as succinct as possible. Also, your resume could include what you are currently involved with. If it is a job, your resume could contain a description of the job you currently are pursuing. If you have interned somewhere previously and if you feel that this experience will strengthen your chances of getting the internship, then you could add it too in your resume.
The purpose of the resume should be fulfilled without the mention of unnecessary and largely irrelevant details. The resume is what the employer has with him to judge you on. It should give the best impression of you.